problem signing into Apple TV+ account on my smart TV

Roku has had many problems recently with users not being able to sign into the app. The best course of action is to contact Roku support for the issue you are having. They will most likely blame Apple, but it is clearly a problem that started recently for Roku users. If you have already deleted the App and redownloaded it again, it will most likely continue until your TV gets a Roku update over the air or the Apple TV+ app gets an update on that platform that will fix the problem.

Another user (mygreensocks) suggested this procedure from Roku Support staff, which reportedly helped several users.

1. Remove the Apple TV app,

2. Shut off and unplug the TV (or streaming device),

3. Wait 30 seconds,

4. Plug the TV (or streaming device) back in,

5. Reload the Apple TV app.

Else try the Network Connection Reset, as mentioned by user Jarieta.

If the issue persists after that, then please contact the Apple Support staff for further assistance.

Discovered a different workaround. Part of the problem appears to be commercials that play before whatever content on AppleTV+. If you have another Apple device (mobile? iPhone, iPad), start watching over on that; at least get through the commercials. Then launch AirPlay.