Apple watch won't unlock MBP after pairing with new iPhone

I've been using my Apple Watch Series 3 (GPS, Watch OS 7.0.3) to unlock my 13" MacBook Pro (13", 2018 4 USB-C ports, MacOS 10.15.7) since I got the Mac. I just received my new iPhone 12 Pro, and set it up yesterday. Obviously, this involved unpairing it from my old phone, and pairing it with my new one. Since then, I haven't been able to use my watch to unlock my MBP. This is what I have tried.

1) Logged in and out of my account on the MBP

2) Restarted the watch

3) Checked the watch app on my phone, and found it listed 2 watches (both mine), one unpaired. I then "unpaired" the unpaired watch, and found it disappeared from the list.

4) Checked Bluetooth on both the watch and the MBP.

When I did the last item, I found that the watch and MBP didn't see one another (neither seemed to be discoverable). I tried turning off Bluetooth on the MBP and turning it back on. They still didn't see one another.

I know that Bluetooth on the watch must be working because it is paired with my new phone, and it seems hard to believe that Bluetooth on the MBP would suddenly stop working.

Any suggestions on what else I could try?

Thanks in advance.