I played around with this when I got my W at first... I paired it to an iPhone X, activated LTE on it, turned off my iPhone X and removed the SIM card off of the iPhone X and put it on my Good 'ole Galaxy S9+ and all was well, except updates, syncs and management (like changing faces or adding apps, pretty much whatever Watch app does) as stated above. You will need your paired iPhone even if you turn it off and put it to the side. After about a week, I ended up switching to my old work iPhone XR as my personal phone since I couldn't pair my W to my new work iPhone 13 Pro Max and activate LTE as it is from different carrier and it is carrier locked, otherwise I could've added my personal phone's carrier to my iPhone 13 Pro Max using eSIM and had both numbers on the iPhone 13 Pro Max. Like mentioned before, you will enjoy using it stand-alone for a little bit and using the Android features, but then you will miss all the W goodies of using it with the iPhone and come back to the iPhone eventually.
BTW, I am a 100% Android fiend (specially rooted) and I get the frustration and reason why wanting one. I love the features like plugging just about anything USB to them (which iPhone lacks) and having total control of the OS, but I learned to put that aside and use other resources (like a tablet or laptop) and use the iPhone as a ...phone.