How do you move from scene to scene in a game?
Some ways are obvious… you move to the next door and open it, and we have a scene dealing with whatever’s inside.
Not necessarily. IME dungeon crawling often isn't so much individual "scenes" as it is one long continuous camera shot covering their actions in the previous room, their moving to this door, their checking and then opening this door, their checking of this new room, their actions in this new room, their move to the next door... etc.
But outside such a structure as a dungeon crawl provides to play, how do you handle it? Let’s say the PCs are back in town after their most recent expedition.
Do you prompt them? “Anyone got anything they want to sell? You know the market is open until sundown.”
I
never need to prompt for this; and they're always prompting me to tell them what's available to buy!
Between-adventures downtime almost always has some tasks that need seeing to: treasury evaluation and division; training (for thems as needs it); and shopping for things both magic and mundane. This all happens in what we call "rubber time"; we deal with one thing at a time but it's understood they're all happeing side-along; Raven is training while Korgi looks for items and Tulsana-Melkolf-Nesta* get the treasury evaluated. Once those are done...
* - these are all current in-play characters in my game; thought I might as well give 'em a shout out...
Do you ask in an open ended manner. “Does anyone have anything they want to do in town?”
... I'll ask if there's anything
else anyone wants to do while here, while bracing for almost anything as an answer.

Some common things are character turnover/retirement/recruitment, checking in with family and-or friends, information gathering, thievery, follow-up on things left hanging during previous visits here. Usually, somewhere in all this the seeds of next adventure will emerge (if they haven't already), be it by something they decide to do or by something I planted or whatever.
You don’t roleplay every moment of the PCs’ existence, so you must have some means of skipping things. Some way of deciding what to skip and when. What is it?
I'll skip things but only after the players have had an opportunity to not skip them.
For example, if they're walking the six days it takes to get from Torcha to Karnos, each in-game morning I'll narrate the weather. This gives them the opportunity to decide to change course and go somewhere else, or to have an in-character discussion, or whatever (they know they're free to interrupt such narrations at any time) while at the same time providing some background atmosphere**. If I hear nothing, and my dice tell me nothing's going to bother them today, then I take it we're OK to skip to the evening (or even to the next morning), and so I do.
** - the sun might always shine on TV but it don't always shine in my game world.
Whatever it is, once it’s determined, the next thing you do is scene framing.
“You arrive in the outdoor market with just a few minutes of sunlight left. Some of the merchants are already packing up their wares for the evening.”
Scene framing = scene setting, then. Fine with me.