No, it shouldn't. They are semantically different code points. The _whole point_ is that they are semantically different code points (they're from the Mathematical Alphanumeric Symbols block, the purpose of which is for e.g. when you have a formula containing ๐น and ๐ as semantically different characters, where that difference needs to be preserved in copying & pasing, conveyed to screen readers, etc.
> Ooh, here's another one-- if you paste some unicode.style'd text into LibreOffice does it convert it to the "normal" code points and add the relevant styling? If not, it should, otherwise it's broken.
It really, really, really shouldn't, for the same reason as above.
Mathematical symbols are not a replacement for text styles and markup. Trying to make them that will destroy the thing they're actually useful for, the thing they can do that text styling can't do: preserve their semantics when transmitted in plain text (including for accessibility purposes).
This is not styling. It cannot be normalized away. They are semantically different characters.