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.
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.
I lost the ability to have my text messages read to me, or to respond by dictating them. For a short time there was a half-implementation from Tesla that was in no way comparable to CarPlay, but it stopped working for me a couple months ago and I haven't been able to convince it to start working again.
I also used to be able to select music to play, and it didn't require jumping through a bunch of hoops to find it. Now my choices is the streaming that Tesla includes, or Spotify, and the Spotify interface is awful. I bought a subscription and tried it out, thinking I could switch from Apple Music, but after failing repeatedly to get the Spotify in the car to see playlists I created on my phone, and growing weary of Spotify on my phone or computer defaulting to playing out in the car even when I had been inside for hours, I gave up on that.
I also used to use Waze, or Google Maps, or Apple Maps, depending on what I felt worked best. Thankfully the maps built in to the Tesla aren't awful, but the interface is not without its quirks.
Tesla could solve this by supporting CarPlay and Android Auto, but they won't, because they need us to have a reason to pay for the premium data subscription.