@mikekaganski Yes, it is. Text in cells cannot have individual background colors, only the cell can have background color. You are conflating the original issue with a different one, a logical fallacy. Your example is thus also flawed: A2 is only working with the number and you have not indicated a desire for any formatting, likewise in A3 you have defined a format for the cell which would probably override any formatting you want to copy from A1’s contents.
@karolus Yes that’s what we’re after, single-chars Formating-attributes. So maybe a different formula/function is needed.
Yes you guess it!
https://api.libreoffice.org/docs/idl/ref/interfacecom_1_1sun_1_1star_1_1text_1_1XTextCursor.html
It is not, and differences between cell format vs. content format are irrelevant - just because in Calc, just as with all spreadsheet programs, char formatting is absolutely marginally useful feature. It may only be applied directly (or by automation - but then use automation also for copying it), and the whole essence of spreadsheets and formulas is massive calculations. It may only be applied to texts, and spreadsheets are predominantly are about crunching numbers. So having a formatting that is only applied manually, and having a function that would handle that, just goes against the intended use of the software. Yes you are welcome to use it as you like, but it’s your problem that your idea misuses it.
Note that in spreadsheets, the most useful formatting is exactly cell formatting, not individual characters’ formatting. And so, my questions handled mostly the mentioned most useful thing, but your “not indicated a desire for formatting” is… funny. You haven’t an idea how much desire I indicated here in A2. At least no fewer than your screenshot 
@mikekaganski Well mike, just because something is in the margin or marginally useful (to you, or even a majority of others) does not mean it needs to be ignored. That’s a very poor outlook to have on anything.
The whole point of asking this question to begin with was so we can copy character formatting by automation, which is the “whole essence of spreadsheets and formulas” just as you mentioned. There’s nothing against the intended use of the software here.
This’ll be my last reply to you as I don’t have the time nor get paid to debate strawman arguments.
Nobody is paid here. We are all volunteers.
If you don’t like how it works, there are other spreadsheet programs, with price or not. But as I know, no one does what you want, maybe strange for you.
@mariosv No one said otherwise, but if no one was allowed to make suggestions because we didn’t like how things worked, we’d all be stuck on version 0.1 still. Please stop posting irrelevant and unhelpful responses. karolus seems to have a solution, actually, if you are reading. How to utilize/implement it is not clear, though.
You’re saying what can I do or not, too much.
BTW, you con suggest on the right place (which it’s not here).
Or pay for it to be implemented by some developer.
Why? There are one or two people left who actually calculate with spreadsheets.
And your idea could break a lot of older sheets, so need to be switched on if needed - after implementation.
.
Main point: You are lucky here as the “manual” for this site tells:
Feature requests should go directly to Bugzilla as Enhancements
https://bugs.documentfoundation.org/enter_bug.cgi?product=LibreOffice&bug_status=UNCONFIRMED&bug_severity=enhancement
Don’t expect to much however…
@mariosv So only you’re allowed to say what others can do or not? 
If you know where I can suggest why don’t you share it with me and the rest of us?
@Wanderer Ideas can’t break anything. Only how they are implemented. Obviously a separate formula or function that would accomplish copying character formatting would not break anything, as older sheets would not be using it.
To be fair, I didn’t know if there was or wasn’t a feature for this. That is the point of a discussion, to learn things. I’ve certainly learned not to expect much from the community here, unfortunately, so far at least.
and it is still unclear if this feature exists or not. Can’t anyone comment on karolus’s suggestion, LibreOffice: XTextCursor Interface Reference? What is this and how to use it?
btw: copy <strg><c> and paste <strg><v> exists:
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So one could create CopyOnChange()-Macro, wich is called when the Source-Cell is changed.
Your first attempt was not “I need another feature” but “This is a bug, fix it”. Quite different approach.
It’s the specification of the API, which may be used to implement an automation (that you claimed you wanted, when explained your XY problem); automation means “create a macro, or extension, or control LibreOffice as a “server” externally - e.g., using Python/VBS/etc.”
Never use various manual/direct formatting properties in a single cell.
Use the cell styles. It is enough to highlight a calculated/referenced values.
The spreadsheet softwares are not colorize books for children.
For examlpe:
There are some well usable workarounds for the more exact referencing of the special formatted characters:
- Sub- and supercript characters what use the upper/lower index formatting feature: use real sub and supercript characters instead of the modified (shifted, reduced size) “normal characters”. The full featured UNICODE Fonts have sub and superscript characters. (Typical usage: the referenced engineering units, like the kg/m³. A shifted/reduced normal caracter “3” will be referenced as kg/m3, but a real superscript craracter “³” will be appeared as kg/m³ when you referenced it from an another cell.).
- You can apply a Cell style by using the function STYLE() at end of the formula.
- You can apply the conditional format feature - depending on the cell content.
But you can not apply different direct formatting properties for the parts of a single cell content by the built-in features in any spreadsheet software. Not in Excel, nor in Google sheet, nor in AOO/LO, …
You must use the copy/paste feature, or you need to repeat enter and format the content in an another cells.
And you can not format manually a result of a very simple CONCATENATE() function this way in the target cell.
I think the closest analogue is Excel Camera Tool. A graphical object is created whose data source is the original cell range.
Funny how such a basic question and possible solutions brings out all kinds reactionaries that don’t want anything to be done, and are actually hostile towards coming up with a solution!
@karolus Yes of course! Silly us, why even use functions at all when we can manually copy and paste hundreds, if not, thousands, of cells. In fact, better to never use any function again since we can do all the calculations on paper with pencil and abacus and then type the result into the sheet afterwards… 
@Wanderer Yes I see, now you are at least hinting at something useful… did not know about Macros so will look into this further. but you still seem to like to put words in others’ mouths. Fortunately on a text based communication platform, everything is clear and can be verified. I never was so coarse and demanding to say “this is a bug, fix it”. Instead, Miguel first replied that there “is no way”. I followed up with a question as to why, so I could better understand any reasoning behind leaving out such an option/feature, only adding that it “seems like a bug”. When Miguel further solidified his position that there would never be any solution, and in fact the problem was with me, I was left no other choice than to pursue filing a bug report–quite a different reality than you paint! (Little did I know the flurry of reactions such an innocent quest would manifest)
@Zizi64 With an imagination like that, maybe you’re the one that needs coloring books? Not only did I never mention color in my OP, but we aren’t even using any color for this particular project. Even so, teachers do use spreadsheets as coloring books for children, so you are even wrong on that front too! 
I don’t think anyone appreciates attempts to control what we can do with the software’s already-existing capabilities. If you don’t want users applying per-character formatting, then you are welcome to fork the project and remove that along with all the other features you don’t want others using. Wonder if there will be any code remaining?
But I will thank you for mentioning Unicode, that is an idea worth looking into as we might be able to adjust the final display we are trying to achieve. Now after having spent some time looking through the characters, I’ve found similar letters that might replicate my example in the OP. However, the problem is finding the right font to render it all. Calc will only render the text using the single font assigned according to the cell’s formatting; if there are missing glyphs, then they aren’t rendered or just show up as squares. This is different from other applications which will just combine the fonts so all glyphs requested are rendered. Fortunately, after a while, I found Symbola will display everything, so was able to get the results below. Unfortunately, there is not enough variation in the sizes of the different scripts, and what we really need for this project is the ability to have text in different sizes like I showed in the OP.
@sokol92 errr, wrong forum? Nobody here is using Excel. I can’t see any of the example screenshots either, plus having an image in the spreadsheet instead of data in the cells themselves is a completely different use case.
I think that takes care of everyone then. Now on to the post where someone actually seems to have found a solution…