This seems to be a caching issue and is inconsistent. I've had instances where the message doesn't display when the start time is reached, but more often it doesn't clear after the end time occurs. It also seems to depend on where you place the block, it works better when placed with Layout Builder, but not when it's placed in another theme region. Debugging the code, the cache seems to always be set to -1, which is permanent. Not sure how this could ever work with multiple messages starting and ending at various times.
Create/edit a message, setting the publish date/time a few minutes ahead of current time, and unpublish date/time a few minutes after that. Place the Notifications Message block in both a Layout Builder page, and another theme region. Refresh the page at the start time, if it doesn't appear, clear caches and it will. Same when the end time is reached. The LB instance may work, but not the other.
Add a getCacheMaxAge() function to set 0 seconds for non caching.
Creating a fork here with the code change.
Needs work
1.0
Code
I'd like to see if there is a more performant solution than setting the caching to 0. It would be better if maybe: