My car is a little psychotic, perhaps :-). Probably a coincidence, but I also can no longer get the dashcam to work. Tried an exotic solution first (Pi Zero emulating a drive, with WiFi uploading at home), but it wasn't reliable, so then I switched to just a regular USB drive (adapter + high endurance microSD card), which worked for a month or so, but has stopped working and I haven't been able to figure out why.
I'm hoping the newest update with the Sentry updates will fix that last problem, since apparently it can format the card now. Though I did hear something about the last release also screwing up sentry for some people, so who knows. I'm at 2020.16.2, so there's at least one more point release that I haven't gotten yet.
I've read in some recent threads that this method ended up resolving a lot of really weird and random issues like what you described.
Out of curiosity, which Tesla? Because iirc there was a firmware update pushed out closer to the end of last year, which added that functionality (both having texts read and being able to respond by dictating), and I thought it went out for all Tesla cars.
The only reason I asked about the specific model you drive is because I know that some older Model S and X cars receive slightly different versions of firmware updates than newer ones like Model 3, but afaik the differences are usually related to autopilot/FSD features, not to UX features like this.