It's not the Watch, it's Tunein. It hasn't been optimized for the latest iOS updates.
The same thing is happening on CarPlay. If you got to your 'recents' they're not there. All that is left is empty templates with no data. The watch no longer shows 'recents' at all.
Want proof? Go to your mobile version of Tunein. Open it. Go to the browse option. See the little car logo up top? Thats car mode. Select it. This is what you see on CarPlay.
Now go to 'Recents' on your Tunein app while in Car Mode. The recents are gone. If you use it as much as I do, you'll see empty blocks where the station ID's should be. The empty blocks still hold the recent but if you're driving, you're still forced to use your phone. The same on the Watch. You need to hound Tunein. Not Apple. Apple only forwards our messages. I sent this to Tunein and got their canned response - "we are aware of the problem and are addressing it in a future update' is the response. obviously it's not a critical update or they would have fixed it by now. But they haven't. Either use this time to hound them and make then update it NOW! or delete the app and try a different one.
Tunein became popular over-night. it can loose that popularity just as fast the more other developers know about the inconvenience to subscribers.