i mean, the immediate first thought here would be expertise dice. but an expertise die to AC/attack rolls seems...much (it's equivalent to about a +2 magic armor/weapon, mathematically). an expertise die to damage is more in line, but is kind of strange and only really works for weapons. still, as a weapon-only thing it's somewhat better then the +1 to damage suggested here mathematically (and in the last thread), if that's what you want.
for armor, i like how the first shot at this topic approached it, effectively giving the appropriate armor master feat (or something in line for such a thing, in the case of light armor) for whatever armor you've doubled up on. i don't like the proposition of this thread as much, mainly because it means you only have that sort of benefit for heavy armor (and i guess light armor in a way), whereas medium armor can be further improved with medium armor master. it feels less consistent. that said, it also feels inspired by pathfinder 2e, which has damage reduction for medium/heavy armors you've specialized in.
personally how i'll probably do this for my games is to take the original approach, except actually giving the appropriate feats for medium/heavy armor, and then for shields giving the shield focus feat. i might change the +1 to damage to an expertise die to damage, if only because i like expertise dice. they go clack.