You can't get MissingNo in Sword and Shield. MissingNo is a Gen 1 glitch Pokemon, and it does not exist in other generations. You can trade MissingNo to a Gen 2 game, but it does not take the same form as it does in Gen 1.
Pokemon fans have unfortunately chosen to name several glitches/ exploits in Sword and Shield after MissingNo. Any glitch Pokemon that you receive through such means is not actually MissingNo.
To answer your questions more directly, there isn't really a 'glitch Pokemon' (if you can call them that) in Sword and Shield so enigmatic that its gets its own unique appearance or whatnot. What you'll find instead are perhaps described better as 'Pokemon with abnormal features', and the game generally has good error handling for those. Their precise traits vary by circumstance and there is probably more research that can be done about their behaviour in situations like Max Raid Battles.
What you can be confident about is that they won't corrupt your save data — most glitches don't do that, including MissingNo itself in Gen 1 (which, contrary to popular belief, is a very stable glitch Pokemon).