https://forums.garmin.com/outdoor-recreation/outdoor-recreation/f/descent-g1/295971/trying-to-add-card-in-garmin-pay-gets-error-having-trouble-communicating-to-our-servers/1507179#1507179
I am having ongoing issue with my Garmin Venu that matches the one described in the linked discussion, so this seems to be generic problem not related to any specific watch.
The problem started when my phone and watch suddenly lost their pairing. I removed and repaired the watch in the mobile application to fix this. After doing that, Garmin Pay had lost card it had previously and all attempts to re-add it have failed with "Sorry, we're having a problem communicating with our servers"
I have tried:
1. Removing the watch from Connect app and re-adding it - couple of times.
2. Restarting watch, restarting phone.
3. Resetting Garmin Pay by changing the passcode and choosing "I have forgot my passcode" - also multiple times.
What I haven't done is remove connect app completely and reinstalling it and resetting watch, but reading other threads these doesn't seem to help. Some reported having done new Garmin Account to get around this, but it just seems daft, losing all your history data to MAYBE gain functional Garmin Pay.