How do people handle other skill ... umm ... ability checks with proficiency bonus such as arcana, history or religion? BTW: the reason I and my table still refer to skill checks is simple. Ability check modified by proficiency just doesn't roll off the tongue. If there's a better way to refer to an ability check modified by a proficiency feel free to chime in.
But take an example. The group is looking at a McGuffin. In my game someone could ask for a history check to see if it had any historical significance. Maybe it should and I didn't think to ask the players for it or forgot that anyone was proficient in history, so I go ahead and let them a roll.
It's obvious what they are doing (wracking their brains for information related to the McGuffin. How? Approach? I'm not sure how anyone would phrase that.
At my table these are often done by the player asking a question like "do I know anything about... " or "do I recognize anything..." and a reference to a check - but just as likely its something like "can I tell anything with arcana" etc.
Sometimes if there are specific bits they are curious about then they will zero in with more detail "those purple snd yellow Rose's, are they like anything specific in the Chauntean lore - roses are big there" That is after in the fiction the Chauntean Rose's has been introduced of course.
So, for like general "what does this mean to me, given my expertise" very little is asked - kinda like just asking for more detailed description. But if there are particular clues they are honing in on, they identify more precisely.
That's the vast majority of our play cases, not just from 5e. I mean, it's not like skills for knowledge, hunting, spotting, investigations etc hsvdnt bedn implemented snd used alongside "abikity" or "atttibutes" for decades in countless games, right? 5e does not have dome magical new thing as far as skills go that deserves scripture status.
I did have an experience where at one table - not sure if it was just one player or a GM thing - where a player would take time to always wrap these in a backstory wrapper - "I will think back to my days studying at the blah blah mountain library and lectures from old msn blah blah about monsters of the south hills and see what I recall about trolls."
I also have had players who went really heavy the other way- giving a lot of out of character explanation of the reasoning as to what he thought and why it made sense and what he was expecting at many many many cases of tryingbyobuse his skills for knowledge. At times, I did have to stop that, interrupt and get on because it was becoming an issue and was unnecessary. To be fair, I think he had issues with fear of failure and getting "gotcha" etc ftom som prior gaming experience, so it was a thing we had to work thru.