I haven't the chance to play PF2e yet, but as I DM the exploration mode options was on of the things I was think about porting to my 5e games. I would be interested in hearing how it works. Thank you for starting this thread.
Your welcome:
There are many ways in which exploration mode is used. I use it for overland travel and local area exploration, switching between the two and encounter mode dynamically. Exploration mode has basically a mechanical interface for switching to encounter mode that works pretty well.
Let me give you an example of how it works in practice for me. The players are F, V, D, Sh, and Sc. They have recently reached safety from a strange skull headed monster in a hunting lodge. This is a horror themed game.
GM: okay next turn, you only have about 6 turns before sunset, you have secured the door, and the snow is still falling, what are you going to do? (I go around the table from me clockwise)
F: I am going to head upstairs and see if anyone is there and make sure all the windows are secure.
V: I’m going to use detect magic.
D: I’m going upstairs with F so he doesn’t get killed again.
Sh: I’m going to go to the kitchen and see what supplies there are, and try to get the fires going if there is any wood.
Sc: I’m going to look at the books in the library to see if they have any information on the snow monster.
I then go through and resolve the actions in the most interesting order for me. I might, for example, start with V who detects magic from the library, then transition to Sc and resolve his action in the library (interacting with a research subsystem most likely). If necessary I drop into encounter mode: lets say, for example, that F and D find a creepy doll upstairs that is actually a monster. When that happens I look at the exploration mode actions that hook into the encounter mode and choose the most appropriate one. They are probably Searching so they get free seek actions to seek, potentially spotting it before it attacks. If they call for help I will let the other characters enter the combat if I think they can hear them or if they retreat to them. Once combat is over I transition back to exploration mode.
Travel mode is basically the same, except turns are longer and the party tends to stick together more. Behind the scenes I have a hex based movement system setup so I can easily determine how far the party travels (they don’t know about the hexes) and if anything interesting happens. If something interesting does happen, they find a mangled and frozen corpse for instance, I switch down to local area exploration mode.
Note: I am omitting a lot of narration here, this is just the bare bones structure. I generally try to limit discussion based on turn length - overland I allow a lot, while area exploration I allow less.
Edit: added note and joke.