In my case I actually can't properly pair the device at all. I hadn't used my watch (Fenix 6 X) in many months, and last time I used it was with another phone.
I went to pair with my Pixel on Android 14 and the actual bluetooth pairing works fine -- shows up in the list of Bluetooth devices -- but the Garmin app refuses to add it, thinks it can't talk to it.
So the phone / watch connection can never happen.
I suspect Google has made changes to bluetooth stack yet again and the Garmin stuff simply isn't working with it. (TBH their apps seem pretty janky)
I always have to go to the gear menu on my phone, Connections -> Connectivity -> Phone -> Pair Phone to put it in pairing mode in order for the Garmin Connect app to detect it. The bluetooth pairing alone is never enough for me, it seems to pair successfully but then like you mentioned, the app never talks to it.
Oh, I'm doing the pair process through the Garmin Connect app. I put the watch into pairing mode, then go to the app. The app sees the watch, then Android prompts for the bluetooth pairing code. That succeeds, the app goes into some sort of state of talking to the watch -- the watch switches to showing a little logo for the app even -- but then the app cacks out saying the pairing was not successful.
Something is going wrong with some internal state transitions, or it loses connectivity while doing some sort of data sync or something.
However, I am back to having to re-pair my Garmin Venu 2 Plus watch every day after some Pixel update a few months ago.
It was broken in early 2023, then they fixed it, then broke it again :( https://www.reddit.com/r/GarminWatches/comments/12hpk0c/venu...
I can't help but think they do it deliberately, in order to drive folks to the Pixel watch.