I encountered similar issues as przemyslaw.leszczuk and wanted to share in case it helps others. I also use Nabu Casa for my online connections.
Initially, I had no problems after installing it on my watch (Instinct 2). However, it started randomly cutting out shortly after without any error messages. I checked my links and API access using the tools in the troubleshooting guide (thank you for those!) but couldn’t identify any issues.
Eventually, I realized it seemed to be linked to opening and closing the Garmin Connect app on my iPhone (iOS 17). Things worked fine on my watch until I opened and closed the Garmin Connect app, which is when the issues arose.
Since then, I’ve kept the Garmin Connect app open in the background on my phone, and I haven’t experienced any more problems with the HA app on my watch. I can open the Connect app and check things without disrupting the HA app on my watch, as long as I leave it open in the background.