Fenix 6s Pro and Google Pixel 6

Since changing to the Pixel 6, the connection between GCM and the 6s Pro has been horrible. 

The phone keeps dropping the pairing, so I'll suddenly see a 6 digit code on the watch with a pair request on the phone, this pairing request will often take 3-4 attempts to succeed, but then will drop again sometimes within minutes, other times longer. 

Restarting the watch doesn't help. Restarting the phone either. Forgetting the watch and re-adding hasn't worked (it just needed to be set up from scratch again, GPay and so on). 

I've updated the watch to 20.00, but that's not had an appreciable effect. 

Possibly as a consequence of the extra load on the Bluetooth seeking, the battery life on the 6s is awful. With an average day being 90 minutes with HRM and power meter I am barely getting two days from a single full charge. 

(My previous phone, the One Plus Nord, had been fine, so I'm prepared for this to be something new in the Pixel 6/Android 12 that Garmin haven't caught up with - although they really should be better at this.)

Any advice?