VideoPress: review proper handling of the isFetching state for playback tokens

While working at #27136, we got some comments about handling the `isFetching` state for playback tokens. The suggestions were:

* review the naming of the state to relate it further with the playback token (something like `isFetchingPlaybackTokens`)
* move the flag from the root level of the `playbackTokens` store to the video objects on `videos.items`, since the token is something highly correlated to the video itself

We need to address the comments and review how we handle this state, to make sure we are doing on the most useful way.

Start by tracing the playbackTokens store and the video objects under videos.items, using the discussion from #27136 as context. Review whether the isFetching flag should be renamed or moved to each video, and consider the work done when the state handling addresses those comments consistently.

Written by the indexing model from the issue text.