No Gaps for the Letter U
The letter U has no exceptions. Every bold, italic, script, Fraktur, double-struck, sans-serif and monospace form sits in the Mathematical Alphanumeric Symbols block (U+1D400 to U+1D7FF), so a whole word set in one of those styles keeps a consistent look. Other letters are not as tidy: script B, Fraktur C and double-struck N, for example, live in an older block.
Small Capital, Turned and Other One-Off Forms
Small capital U is แด (U+1D1C). Like most small capitals in Unicode it was encoded for phonetic notation, not as a font feature, which is why small caps text pastes as ordinary characters. Unicode has no dedicated turned u, so upside-down text substitutes a character that already has the right shape when flipped. Superscript u is แต (U+1D58). Subscript u is แตค (U+1D64). The regional indicator ๐บ is half of a flag: two of them in a row turn into a flag emoji when they spell a country code.
Which U Is Safe to Paste
Bold ๐, italic, sans-serif and monospace forms display on nearly every phone and computer. Circled โ and fullwidth ๏ผต are also widely covered. The squared and dark squared forms of U have no emoji version, so they stay black and white. Screen readers may announce a styled U by its full Unicode name or skip it, so keep anything important in plain letters as well.