You could dump it to some website or an app on your computer, but that feels like much the same. For me it depends on the implementation. It the watch continuously push data to the phone, then yes, BUUUH!

What I'd love is a fitness track, without a subscription, that sync data with HealthKit whenever my phone is within reach, but buffers it, if it can't find the phone nearby. It's the assumption that my phone will always be with me when I workout or take a walk that triggers the "BUH" from me.

I'd also love for this device to not be a watch, because that limits my choice in which watch I can wear.

It sounds like you are describing a Garmin watch.

It uses an app to sync with Apple health but will happily run offline for a week until you can sync it.

There are also heart rate bands you wear around their chests since you mention non-watches. I am not sure if those will work without another device to sync with though.

You can use a Polar watch if that's what you're into - I used a Polar Pacer Pro for a while that you can sync to a computer periodically, or just use it offline.