Regular expressions: replace with tab (\t) doesn't work for me

I’m performing a simple Find&Replace: search for paragraph breaks ($) and replace with a paragraph break followed by a TAB (so as to indent all paragraphs manually with hard tabs, instead of using the indent function – don’t ask why).
It doesn’t work. I do Find $ & replace by \n\t.
But what it does is just type “\t” at the start of each paragraph.

Whereas here it says:
“Represents a tab. You can also use this expression in the Replace with box.”
What else do I have to do? Why doesn’t it work like this?

Also, I’m a little confused in the link above by the peculiarity that to search for paragraph breaks you have to enter $, and to replace them you have to enter \n.
How does this double function of \n work if you would want to search paragraph breaks and want to replace them by line breaks? Is that not possible in LibreOffice, or is there yet another symbol that represents a line break in the replace box?

Hallo

Use search ^. replace \t& instead.

Karolus

To add to the answer by @karolus, regular expression engines are generally line-based (in LO paragraph-based), so performing find/replace across a paragraph boundary (outside ^ and $) is usually not possible.