Specifically, do they proc “per swing” or the game calculates it seperately for every enemy hit?
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Yes and no. It’s per swing, but it will then crit on every enemy hit, potentially giving you multiple crits (which may proc talents or blessings).
Great and important question! They’re always counted per attack. So either all targets hit with the same swing / shot / explosion / puff of flame etc get crit… or none of them will.
Naturally this greatly affects talents etc. since slow but big AoE attacks are no more likely to get even a single crit proc no matter how many targets they hit at once. But on the other hand, if you can force those crits with talents or ults, they become all the more meaningful.
Edit:
I’d also add on crits, that Purge staves and Flamers apply 2 DoT stacks on crits instead of 1. All DoT’s also have a logarithmic dmg curve where from 1-4 stacks each doubles the dmg before it, and from there tapers down to +50% dmg each, and finally ~15-20% each at 13-15 stacks going still slowly down from there. Because those DoTs reach horde/special+ breakpoints on ~6/8+ stacks getting them up fast is important, effectively making them all crit weapons. 
Oh and also, in case you want to make use of Zelly’s stealth, note that it has a small 0.5-1s insurance duration when you use it, where it won’t break even if you attack. So you can for example charge a heavy swing, use ult just before attacking, then attack & get the full crit & finesse bonus from it, and your stealth will still stay on for its full duration letting you do another attack later. With fast weapons like knives you can even just tap stealth while spamming with the weapon and you’ll get off 3-4 autocrits before it wears off. Super handy in case you want to make a crit build that way! I love that trick with my cleaving melee or for example the Kantrael shotty with Man-Stopper & Flechette, letting me pull off 2 autocrit specials for massive burn & bleed stacks on everything in a huge area.
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On melee it’s per swing. You don’t have to hit anything. You will get a crit swinging at open air.
You can verify this yourself with Perfect Timing talent on the psyker tree. You can gain stacks without hitting anything.
For ranged it depends on the fire rate, but same deal. You can crit without hitting anything.
To further elaborate on the fire rate statement; you get crit batching mechanics based on the fire rate. Doesn’t seem to have a mathematical formula attached to it to determine how many crits are allowed per single proc based on fire rate, but as an example Recon Lasgun VId shoots at 16+ shots per second and the crit batch means a single critical proc gives you 5 criticals.
This means even just 5% crit on high fire rate guns are disproportionately strong.
As an example if you use MK V Columnus (crit batch value of 4), and you don’t build crit on at least its perk you are wrong. Plain, and simple.
And some crit proc effects have an undisclosed internal cooldown, for example, the recon’s crit for 5 shots at a time, but only procs infernus and shock trooper once.
There was a dev post regarding dots and exponential scaling a year ago, still worth a glance.
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It’s not just shock trooper that got nerfed with an internal cooldown, the crit salvo on weapons changed too, AFAIK the Steam guide is up to date.
The Recons now have a crit chain of 2.
P.S. Note that some weapons have an inherit crit bonus and others a -2 penalty, add that to the archetype base chance (see guide) .
Consecutive crits per crit chance trigger (ranged only).
This essentially means that when you trigger a crit within a salvo, you will get X more crit shots in a row but then X shots after will not crit. it would not affect pseudo random crit chance.
Recon Lasgun(mk2): 2
Recon Lasgun(mk6d): 2
Recon Lasgun(mk7a): 2
Braced Autogun (all): 3
Infantry Autogun (mk1): 3
Infantry Autogun (mk5): 4
Infantry Autogun (mk8): 2
Auto Pistol: 4
Ogryn Heavy Stubber: 6
Flamer/Purgatus: 3
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Well that figures. 
While I’ve played since release, I’ve only been active here on Fatshark forums for a few months I think. DoT’s like basically everything else was just stuff I had to go and test and figure out on my own. But it’s no surprise if that stuff is hidden behind random posts and not obvious in the game.
There’s a million things that aren’t explained in the game after all, so even to date from forums to the game itself, it seems like none but the most avid endgame gamers know how most stuff works. On the other hand, that’s also part of Darktide’s charm. Being curious, testing and finding things out is actually useful. Where most games are just boring cookie-cutter meta with no exploration or hidden little secrets left. 
Also DoT’s are not exponential as explained there btw (tho the dev’s dmg per stack example does show this, so that’s ok), it’s logarithmic. Like so:
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Oof. Recon definitely holds its title of most nerfed weapon in the game.
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I’m pretty sure they changed this, it’s no longer 5 but 2 shots for the Recon Lasgun now But conceptually you are right.
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