I didn't realize this. Just verified on my Forerunner 965, if I put my phone in Airplane Mode, turn off Wi-Fi, leave Bluetooth on, then Garmin Connect disabled the sync button and says "No Internet connection".
This is why when Garmin Connect has outages you can’t sync the watch to the phone, it’s a pretty bad architecture. It should sync to the phone without internet or any services and then use internet to sync from the phone to the cloud.
It's utterly bizarre. I was impacted by that outage a year or so ago and they claimed that they were going provide offline syncing in the future but I still don't see it. It seems the flow is Watch ->(Bluetooth)-> Phone ->(LTE/WiFi) -> Garmin Cloud ->(LTE/WiFi) Phone. There's no reason for the Cloud step other than that Garmin wants your data but the sync won't work without it.