I've used Beddit, quite good but company has been bought by Apple and I don't think it will ever get any updates as a standalone product.

The most advanced and exciting one is probably the Dreem headband, an EEG that also has features to fight insomnia and even attempts to improve your deep sleep : https://dreem.com/en/

Quite pleased with it, even though the app still has teething problems.

I used to use the Jawbone UP because it had the best REM sleep tracking. I bought up a ton of old ones when they closed down because they don't last.

I use the fitbit now. The sleep tracking has caught up.

The link between REM and mood/clarity is very strong in my case.

Is there one which doesn't upload your habits to the cloud?

not that I know of. The devices themselves were very fragile and undependable. The new generation is reliable though. But in the old days you had to have a backup somewhere or else you lost all the data.

I just have the very cheap Mi Band 2. I don't know how precise it is, but it really tracks the amount of sleep I have.