Wear OS: can't register second device

**Home Assistant Android app version(s):**
Current non-beta?
2023.8.2-full

**Android version(s):**
12 Galaxy S10+
2.44 Fossil Gen6 1842
4.0 Galaxy Watch6 Classic

**Device model(s):**
Above with versions

**Home Assistant version:**
2023.7.3

**Last working Home Assistant release (if known):**

**Description of problem, include YAML if issue is related to notifications:**

Adding the Fossil worked fine months ago. When I try to add the new Samsung watch, it goes to the login page as usual, but the "manage device" page where you name it shows up as the other watch's name, and then takes me back to the login page regardless of if I change the wearos device name or not.

**Companion App Logs:**

There is no "settings > companion app > show and share logs" option. 🤷‍♂️
```

```

**Screenshot or video of problem:**

**Additional information:**