I had mild speech problems as a child that mostly cleared up. Now in my 30s, I developed a stutter about a week after a positive covid test. I'm considered a "long hauler" so I've had a bunch of lousy side effects, but the stutter is one of the weirder ones. I posted on a few long covid groups and there's quite a few people that have been infected and struggled with speech. I haven't heard of anyone who only had the vaccine and started stuttering, but it doesn't surprise me (not antivax, just observing). I also don't see any explanation as to why. Even my doctor was like hmm... But I've seen people talk about it and they regain their old speech patterns after a period of time.