I'm not diagnosed, but I stim a lot. When I'm happy I shake my wrists or flail my arms a little and sometimes I bounce up and down. When I'm stressed I rub my hands together in a regular motion and/or scratch myself (arms and neck) and swing from side to side. I also rock a lot, both when happy and stressed. When I eat something I like I kind of wobble the spoon or fork in my hand and as a child I used to hum while eating, but I've since stopped doing that. Something I always do no matter my mood is tapping my fingers to the music that's currently stuck in my head (I always have a song playing in my head or sometimes sentences or funny sounding words, idk why). I used to try and suppress those stims, but I'm much happier now that I mostly embrace them (at least when I'm alone or with people I trust).
I don't get annoyed by the repetition, I actually enjoy it when it's interesting sounding words or the way a sentence was said was funny wo me when I first heard it. Conjugational recombination is a great word, btw!
The only theory I have is that it might be a form of echolalia, where instead of repeating words out loud you just do it in your head (maybe something like supressed echolalia? I've heard some people online say that it can present that way, but idk how generally accepted that idea is.) As far as I know echolalia is also a symptom of tourettes. I don't know if it can also occurs in allistic people.