I would like this same thing just without the trim

I have the push-to-open latches on my bathroom cupboard doors and drawers. I bought an extra set for drawers because they sometimes stop working. So I have a spare set of drawer glides, just in case. Any good cabinetry supply should carry them.

You can place art over it

Google ”recessed picture frame medicine cabinet.”

Your solution is to have panelling on the wall and cabinet door or an appropriately patterned and well-adhered wallpaper.

Just cut out the drywall and finish the edges with metal and drywall. You will still see a seem but will be flush with the wall. Maybe google access panels.