AFAIK, the general approach to playing HLS is that you (as the client) don't know anything about the content of the Master playlist.
That means it would be pointless to tell you about a problem fetching a Media Playlist - it's way below the level you can see.
Instead, the Master Playlist should contain multiple variants with the same (or nearly identical bit rates) so that when one is unable to be fetched, it can switch to another. That puts the error tolerance down at the framework level.
Here's what I've ben told in the past about HTTP erorr codes vis-a-vis playback:
In general, HTTP errors (other than 410) will put the variant stream into a 2 minute penalty box. A 410 will remove the variant from the list permanently.
A 404/410/5xx from a media segment may cause us to skip the segment and move on to the next.
Unless the stream is unmuxed, which case we will stop playback immediately.