I bought a Pixel Watch 1st Gen. about a month ago and was very sceptical about all the privacy implications. Especially location and bluetooth tracking are something I don't like, yet offer the best functions and reasons to use a smart watch. I specifically wanted it for notifications (not necessarily phone calls) and navigation. Unfortunately, the Watch App needs network for those and play services needs at least the Nearby Devices permission to even connect to the app - even when the phone itself is connected to it via bluetooth, the app requires play services to have this permission. I really don't like that.
I don't know how you would transfer custom apps to it, but I know it is possible to enable developer options. I don't know how good - if at all - fitbit sync would work without network, but I think everything in Critical and Important except Navigation would work without network.
I'm not sure if I'll keep it. Maybe I'll try out a watch with asteroidOS. Have you looked into this? According to ChatGPT the LG Watch R or LG G Watch Urbane would meet your requirements when paired with AsteroidOS.