iPhone 12 Pro: Apple Watch pairing stuck on update

UPDATE: After a few days, I'd decided that I'd try pairing again. This time, after hitting the "Start Pairing" button, the next screen told me that my phone had been paired with my watch. I followed the rest of the setup steps and my phone is now fully paired and synced with my watch. I vaguely recall a comment on Reddit now addressing a similar issue, advising that giving it some time, sometimes, is the solution, as frustrating as that may be.

Some other information that may be relevant is that, while the watchOS update had been paused, I left the house many times and had even had my phone run out of battery multiple times, which I thought would've reset the pairing process. So if you're running into this issue and want to try giving it some time, don't be afraid to leave the house and the watch alone.

While I can't exactly pinpoint what exactly switched to allow me to continue the update, I have a theory: my phone running out of battery, essentially resetting, and then turning back on to connect to the internet might have allowed me to get past the issue. Before, I had been unpairing my phone and watch and then resetting both, so maybe only resetting my phone while keeping both devices paired resolved the issue? Either that, or me physically moving to another location and then returning to connect back to my WiFi resolved the issue?

TLDR: For those who have run into this issue, and those of you in the future who may run into this issue, just give it some time. Don't put your day on pause for this update. It might just end up resolving itself.