Google Pixel 6 will not pair or stay connected over Bluetooth

The checks in more detail

Make sure the accessory is charged, because a low battery produces a weak signal and odd behavior, and keep it within a few meters with no wall between you and it. For a car, delete the phone from the car's list as well as the car from the phone, then pair again, and check the profile choices in the device's gear menu, where Phone audio, Media audio and Contact sharing can be switched on or off; a missing tick on Media audio explains calls that work with no music.

Interference from Wi-Fi routers on 2.4 GHz and from USB-C hubs near the phone can disturb the link, so test away from them. For earbuds that cut out when the phone is in a pocket, the body blocks the signal on the opposite side, and moving the phone to the same side helps. If the phone has been updated recently, check for a newer update, since Google fixes Bluetooth bugs in monthly patches. As a last step, reset Wi-Fi, mobile and Bluetooth in Settings, System, Reset options, which clears all pairings, then pair again. If a device fails on every phone, the accessory is at fault.

If every accessory fails only on this phone, ask Google for service. Older Pixel 6 phones that have been through many updates can carry stale Bluetooth data. Clearing the cache of the Bluetooth system app is possible in Settings, Apps, See all apps, Show system, Bluetooth, Storage and cache, and it removes pairings, so note the devices first. This is a milder step than a full network reset and fixes a surprising number of stubborn drops. If you use several accessories at once, such as earbuds and a watch, test with only one to see whether the number of connections is the issue.