Okay, I started datamining. Here are 10 8 quick and dirty lists of the highest checks under various circumstances.
Watcher, party assisted
Alchemy: 15 (decipher notes for the +stat cauldron)
Arcana: 19 (conversational fluff with Bekarna)
Athletics: 15 (grab Neriscyrlas' phylactery unharmed - I doubt this one is actually Watcher specific)
Bluff: 20 (feign loyalty to Nemnok)
Diplomacy: 23 (negotiate with the mad spore in TFS)
Explosives: 17 (disarm the Godhammer in BoW)
History: 18 (declare contract illegal in TFS, probably avoiding a fight with the vithrack boss Sissak)
Insight: 20 (...some TFS puzzle?)
Intimidate: 22 (convince the Slaying Face to back down)
Mechanics: 12 (conversational fluff with the belt quest NPC in SSS)
Metaphysics: 20 (avoid fight over starmetal in TFS)
Religion: 16 (probably-fluff with Hafjorn in BoW)
Sleight_of_Hand: 15 (fake-drink blood in the Splintered Reef)
Stealth: 10 (sneak into naga cave on northeastern island - probably not actually Watcher specific)
Streetwise: 20 (unseen event with the broken wagon on the starter island)
Survival: 18 (mansplain Llengrath to the spore that thinks it's Llengrath)
Watcher, unassisted
Alchemy: 6 (poison the boar for the Survivor challenge)
Arcana: 13 (convince Wael to put their body back to sleep)
Athletics: 15 (enter the SSS arena complex via the well)
Bluff: 13 (something with the Spindle Man vithrack in Delver's Row)
Diplomacy: 16 (convince Wael to put their body back to sleep)
History: 7 (seems to create some kind of distraction to allow a companion to steal stuff in a wild encounter on the southwesternmost island)
Insight: 10 (call out a bluff from the Surviving Face in SSS)
Intimidate: 12 (threaten Wael, but pointless - they won't act differently even if you succeed)
Mechanics: 5 (uselessly try to open the chest that begins SSS)
Metaphysics: 8 (conversational fluff)
Religion: 12 (bow your head to something in a wilderness encounter - unsure of effect)
Sleight_of_Hand: 10 (steal from the camp on the Black Isle)
Stealth: 4 (knock out some xaurip by a shrine)
Streetwise: 12 (cheat in Orlan's Nose ship event)
Survival: 9 (avoid some lagufaeth trap)
For the next two: Initiating party member means you start an interaction in the real world. It's not a scripted one.
Initiating party member, party assisted (both of these are the pustule on the wall in the bowels in TFS, but there might be lower ones)
Alchemy: 16
Sleight_of_Hand: 18
Initiating party member, unassisted
Sleight_of_Hand: 5 (place a bomb in a brazier to try to assassinate some Wahaki)
The next ones should pertain to scripted interactions. Any means it's enough if one member passes. All means everyone has to pass.
Any, party assisted:
Alchemy: 17 (turn herbicide into fertilizer in TFS)
Arcana: 20 (break an enchantment on some armor in TFS)
Athletics: 22 (knock down a wall in TFS - can be done with just tools)
Bluff: 15 (line seem related to the Wild Mare and/or Konstanten)
Diplomacy: 14 (make the escaped slaves on Crookspur Island stop shooting arrows at you)
Explosives: 20 (seems to be for the same wall as Athletics 22)
History: 14 (fluff about the armor worn by the frozen glamfellen near the Vytmadh portal in BoW)
Insight: 15 (something something Fyonlecg TFS)
Intimidate: 16 (make the escaped slaves on Crookspur Island stop shooting arrows at you)
Mechanics: 26 (open the trick lock in TFS - can be done without any skill)
Religion: 15 (seems to be fluff about identifying a wilderness shrine)
Sleight of Hand: 15 (mislead someone during the Slayer trial in SSS)
Stealth: 18 (some SSS wilderness check)
Streetwise: 15 (seems related to finding the chest for Pukestabber)
Survival: 19 (navigating the bog on the northwesternmost island)
Any, unassisted:
Arcana: 4 (seems related to saving a man overboard during a storm)
Athletics: 15 (weird mixup with the similar Watcher-only check in SSS)
Bluff: 8 (seems to create some kind of distraction to allow a companion to steal stuff in a wild encounter on the southwesternmost island, see Watcher, history 7)
Explosives: 12 (blow up a naga totem, probably on a northeastern island)
History: 1 (uhh... do we care? 😛 probably the Wise Teeth Necklace druid on the starter island)
Mechanics: 11 (pin the drake in the SSS grand event)
Religion: 5 (...seems to be some fluff line by Xoti, so I'm not sure about the "any" part)
Sleight of Hand: 10 (steal a dagger from the campers on the southwesternmost island)
Stealth: 13 (?)
Survival: 9 (avoid some lagufaeth trap)
All, party assisted:
Athletics: 19 (enter final boss room in TFS without injury)
Stealth: 13 (seems related to Nemnok's dungeon)
All, unassisted:
Athletics: 8 (climb the gate tower in Hasongo)
Honorable mention for weirdest skill check
There is exactly one check that is hardcoded to a specific party member. During the wasteland trials to unlock the Survivor fights in SSS, there is a party assisted Athletics 10 check that is forced on party member 4.
TODO:
1) Fix eyesore code
2) Datamine context for the checks too
3) Datamine alternative ways to pass checks
4) Make beautiful thread