I think that stock weights used in Pawn come from Wowhead.
As for the how the addon works, it simply calculates weighted sum of stat of given item and compares it using the same method with item you wear. It takes into consideration sockets with assumption you would put there best available gem best on stat weights (or manually configured gem).
You are right - Pawn will not factor Azerite armor, trinkets, set bonuses and won’t help you choose enchants. But as for enchants the best one doesn’t change often, sets are rare in BfA and Azerite armor + trinkets only take up 5 of your slots, so I can still use Pawn for every other.
AMR can of course simulate total amount of stats if this is the best combination to end up with, as pawn will just compare individual items. This of course can be addressed by using Best in Bag feature from time to time. Anyway it’s still more convenient to use Pawn for regular items as it’s just much faster.
Anyway I think I’ve found a way to do an approximation of desired stat weights based on what AMR is suggesting.
I have used this table of gem alternatives:
And put it in the spreadsheet:
I guess it’s the best workaround I can think off for now.