A side-note: i think the title of the thread is not good. I do not see why refresh-awareness (which is a specific feature) is the problem here. Actually it should be the solution for many users.
In my view: The firefox snap should have given you a notice that you should restart firefox (didnt it do this? - would consider that a bug in the firefox snap)
I agree that snap refresh should give a better indication if and why it skipped a refresh. I am actually aware of at least two reasons why new revisions are not available for install/refreshes get skipped (being in a different cohort or snap on hold).
Actually i use a wrapper for snap refresh, which calls snap refresh --list before actually calling snap refresh. So I get a list of refreshables and then I see what actually got refreshed.
Maybe ‘snap refresh does not give an indication that SECURITY relevant revisions are skipped’ would be a better title.