iPhone 16 Pro Bluetooth issues with Apple Watch

Has anyone seen persistent Bluetooth connection issues between an iPhone 16 Pro and Apple Watches?

I’m having pretty severe connection problems with both my Apple Watch Series 11 (daily driver) and Series 7. The behavior is identical on both watches.

The watches constantly lose their Bluetooth connection to my iPhone 16 Pro. If Wi-Fi is available, they sometimes switch over, but often there’s simply no active connection at all. It’s especially annoying when trying to control media (podcasts/music), and even adding Wallet cards frequently fails because the Watch claims there’s no connection to the iPhone...even though the phone is literally right next to it.

Other weird behavior:

• Switching between watches sometimes fails because the iPhone seems “stuck” to the Bluetooth session of the other watch
• Reboots only help temporarily
• In many cases both devices need to stay powered off for ~30–60 seconds before reconnecting properly again
• Case/no case makes no difference

Things I already tried:

• Unpaired and re-paired both watches from backup
• Reset network/connection settings on the iPhone

I have NOT done a full factory reset on either device yet. Has anyone experienced something similar or found a reliable fix?