Gadgetbridge is the only way I’m aware of to use a smart device on Android completely offline. Otherwise I will second Garmin watches, which do collect a lot of data to your Garmin account by default IIRC, but all that data collection should be able to be disabled. I’m not aware of any way to use a WearOS (Android) or TizenOS (Samsung) watch’s fitness features without connecting them to Google Fit and/or Samsung Health which are cloud-based services.
An Apple ID used to be optional but I believe it is now mandatory for the initial setup, could be wrong though. You also need an iPhone.
However, once the Apple Watch is set up you can use it entirely without iCloud integration, Apple Health only operates locally/offline on the iPhone. It does have an option to back up to iCloud, but that can be easily disabled and even if you leave it on Apple Health is end-to-end encrypted with your iPhone’s passcode unlike Google Fit and Samsung Health.
Edit: It’s also worth noting that the Apple Watch is known to be the most accurate smartwatch on basically every metric it tracks, if that’s important to you. I really really like this YouTube channel as far as in-depth looks at various wearable devices go: