I see that there is a 5e Bestiary if I want to run this in 5e, but I can't figure out if the actual kingdom management rules, mass combat rules, and other non-bestiary challenges/encounters will have 5e compatibility/conversions.
I'm thinking of things like traps, Perception checks, influencing NPC attitudes, even a few other skill checks like Society and Crafting -- if I pick this up and the 5e Bestiary, how much further conversion am I going to be on the hook for to run this in 5e?
That will help me to decide whether running in 5e versus getting my players to learn PF2 and running it in PF2 is the way to go.
The Kingdom rules and warfare rules are designed to be system agnostic; they don't directly interface with the other game much at all, so you should be able to use them as-is for any game... although they ARE based on the 2E design philosophy and elements, so a familiarity with Pathfinder 2E will help.
For non bestiary elements in the Adventure Path, like skill check resolutions or treasures, you'll have to do that conversion yourself... I suspect that there'll be forums here or on Reddit or elsewhere where GMs might share their work in that area though.
That's good to know, thank you. It might be worthwhile to add some clarity of language to the 5e conversion guide that it is just the monsters -- at $150 combined MSRP for the two products, I suspect more than a couple of people will erroneously expect to have everything they need to run the game out-of-the-box in 5e: "this volume makes quick conversion of the campaign to 5E a breeze!"