Energy:
Fire/heat
Ice/Cold
Lightning/Electricity
Thunder/Sonic
Force/Shockwave
Psychic/Mental
The "Radiant/Holy" and "Necrotic/Unholy" are secondary distinctions/considerations, I think, individual to certain creatures/special abilities...maybe, if the designers include or want to incorporate such elements into a "general" part of the game, accepted cosmology, etc...if so, they would go under "Energy" types.
Not sure if "Natural Attacks" count as "Non-weapon Damage" for the purposes of the OP, but in case...
Physical:
Bludgeoning/Blunt (fists, tails, various appendages)
Slashing/Slicing (claws mostly, other things like mantis/ankheg forelegs, etc.)
Piercing (certain claws, teeth, certain horns/antlers, stingers)
Toxic (poisons, venoms, acids, chemicals)
Blood loss (whether "passive", a.k.a. "bleeding out", or "active" via stirges, vamps, etc.)
Then there's "Ability Damage" that's kind of its own thing as it could effect mental or physical traits.
"Falling" doesn't really strike me as a valid "damage type" since the damage is from the landing, not the fall. Yes, obviously, the damage must be calculated by the height of the fall, but the Damage type would be different for different falls.
If you land on a flat stone surface -bludgeoning. If you land on a field of spikes -piercing, first, and, most likely, bludgeoning also... possibly with a sprinkle of Toxic (poisoned spear tips) on top.
And "Non-lethal" could/should be taken into account, I believe someone has mentioned the option/idea of this being a "condition", so to speak (gods, I do NOT want "conditions" per se back in the back!). An "add-on" to the base Damage type (cold, slashing, whatever it is).
That would be something like:
Ongoing
Non-lethal
...not sure what else might be a "mitigating factor" to other damage types.
"Focused" maybe?...eg. I cast a spell that does "Focused Lightning Damage." I "focus" it onto the creature's legs...?
"Critical"...?