I'm really interested in how do we even depict incorrect pronounsuations of some sounds

like there's a thing with some people who can't roll their r's like in russian, they are called "kartaviye". I used to do that too, bur somehow learnt to pronounce it.
there's also people who (wow me reference!!! again!!!) can't pronounce L and say like something between nasal n (like the sound that n makes in the word english), russian ы (which is not it's own sound but. this is the best way I can't explain it)
ALSO there's people who can't pronounce rz (Czech sound, like in rzeka (river)), and they do like some weird ass sound I can't even describe

so knowing all that lead me to thinking. if we have standartisised phonetics for the most common sounds. why don't we have any short depictions of all those sounds????? do I make them???? do they exist and I just don't know where to look??? huh????