I have a HA instance that is only accessible from the local network, running SSL under a domain hassio.mydomain.com that is resolved by the DNS present in the network (but not in the public Internet). I could not get the Wear OS app to connect to the instance unless I forced WiFi on the watch - with Bluetooth on it connected without an issue. The moment it got routed via the BT connection - no luck.
I’ve decided to run a small experiment - I’ve added an A record in the public DNS to resolve hassio.mydomain.com to my local IP address e.g. 192.168.1.10 (you don’t need to tell me that this is an anti-pattern) and to my surprise it worked. This means that when the watch tries to access the network over the BT link, it ignores the DNS settings of the network the phone is connected to and uses something hard-coded. Which is a privacy-invading anti-pattern, but there is little we can do about this.
Just as @ng175 mentioned, if your device has any setting related to “Private DNS” disable it - it will prevent your network’s DNS setup from working.
Which device? (Sounds like a weird question)
Phone, Watch, HA app on phone, HA app on watch, HA itself, Pihole, DNS on router. I did try looking but cant seem to find it, and dont know which device to do a deep dive…