That’s really odd behavior, but the new app continues to surprise me on what works and what doesn’t - literally from hour to hour!
If you’re not using any custom DTH’s, then there has to be a sync issue between the 2 apps, and that does happen. Even the new app has it’s own issues showing the state of the device between the dashboard view and a Room or Tile view.
You can actually use both apps, like I do; but keep your automations, Scenes, STHM, mobile presence, etc within the new app. It will save you from confusing which app is doing doing what to your devices. I have Classic installed just to manually control devices through the app and for some of my composite devices that haven’t been fully migrated to support the new app yet, and I haven’t run into any issues. There are a few discussions in the community about the difference and running both together, so I suggest searching from them.
Let’s try something? Keep Classic installed and reinstall the new app. Within either Classic, or the new app, assign your 3310 to a Room. Toggle back and forth between the apps to make sure the device shows up in the Room in both apps (confirms at least some sync’ing is happening). Within the new app, go to that Room and tap on the 3310. What happens now?
If that doesn’t work, long press on the tile and a small menu will pop up. Tap on “Set as favorite”. Go to your Dashboard. You’ll see your Room listed, but now with the 3310 device listed as a favorite. Tap on the tile. Does anything happen?
If not, then I would recommend contacting support (through the app, or via email) and tell them your device you’ve just added is not sync’d correctly. Just make sure you don’t have any custom DTH’s for that device because they’ll tell you to use the stock handler and try again.