When asking here, always mention OS name, LO version and save format. This gives cues for adapted answers.
When you apply Format
>Font
>xxx
to some sequence, you add metadata to your text without modifying it. This metadata tells Writer to render text in a specific manner.
Note that you applied it manually, called direct formatting in Writer. Though it may look “easy” to do so, this is only a means to discover which kind of variant may be applied to text and to experiment. The more professional approach is to use styles. This allows you to control centrally the appearance of your document without the need to hunt for all your direct formatting. It is much more powerful and versatile.
When you copy a sequence, the full sequence and its metadata is transferred to the clipboard. If you paste outside of Writer, it all depends on which kind of format the external application understands. If ODF (the LO standardised format) is totally alien to this application, it falls back to the “simple text” version which is also stored in the clipboard. This simple text is made of the characters with all metadata stripped off.
As I mentioned above, applying a format does not change the text (and this is great because you can change for another “look” without needing to modify text). Consequently, the raw initial text sequence is pasted.
EDIT 2022-12-20
Format
>Text
>UPPERCASE
and the like don’t apply a format but change text casing. It is not the same as applying a style. Use it if you want to really change document casing.