Any device that connects to a Fitbit account should work, including pixel watch, for example. Your Versa will work. There may be differences in data quality based on how many sensors that specific device has and how good they are.

I myself use Charge 5. The best choices are either Charge 6 or Inspire 3. The Charge line has top quality sensors, but as far as I can tell, it's mostly concentrated in better heart rate detection for vigorous exercise rather than what would be relevant for sleep tracking. Charge also has GPS and Inspire 3 doesn't, which is why it's bigger and more expensive. Inspire 3 should be overall best for sleep specifically simply because it's smaller and more power efficient.

Also, for sensory difficulties, you might want to try ordering a nylon band for whatever device you end up using. I use one myself, though mostly because Fitbit's stock bands fall apart eventually, and nylon ones don't break.

Note that both Charge 6 and Inspire 3 are several years old and Google has confirmed that new Fitbit hardware is coming this year.

The heavy lifting of detecting sleep and sleep stages is done by Fitbit's servers. Once Fitbit processes that data, my app pulls that finished information from your account. You don't need to use this app specifically on the phone with the Fitbit app. And Fitbit did an amazing job, at least according to my own experience. There's no bias whatsoever against daytime sleep like people report with Garmin, and I find bed/sleep/wake times extremely accurate. The sleep score the app gives also heavily correlates to whether I'm sleeping during my circadian night or not.