Dark Souls: Eventually he's just unable to advance any further, when the tier 6es show up. Electricity drain isn't the most helpful against things that are already dead, or weird things like ghosts. Random spawn doesn't change much, and given the setting he's not gonna end up with the nicest life. Dark Souls is just an unfortunate place to be.
Magic: The Gathering: MTG has such a large variety of places he could end up that I really can't say. Dargoo wants to downgrade most of the Gatewatch so if that went through he'd have more raw power than everyone else there besides Chain Veil Liliana, which would be neat if he was with that group. Between infinite universes and outdated verse stuff it's hard to say.
Bloodborne: Normal if he's outside Yharnam, Dark Souls like if he's inside it but he might also just look at the wrong thing and go insane due to it.
Berserk (Verse): Being very powerful means I find it likely that someone who messes with causality would attempt to get him to become an apostle through sacrifice to a behlit. RFI means it's hero cole, so he's already decided to not be a villain here so idk how well that goes over without some major pulling of strings. Cole can't really do anything about
Idea of Evil though, since he's not going to eliminate the concept of evil anytime soon especially in this verse.
Cthulhu Mythos: Either something unpleasant happens to him or he lives a pretty normal life.
Darkest Dungeo: With how omnipresent it is, he probably does end up going insane at some point. He could also get unlucky and spawn in the Farmstead, forever trapped within shifting timelines and all that junk.
Destiny: Honestly wouldn't even be that special. Tier 7 is stronger than stuff we use for semi fodder and average guardian, but it's nothing compared to the famous ones up at tiers 5 and 4 and his electric powers aren't that weird in this sort of verse. If he gets a ghost he would just end up a guardian of unremarkable status, if he didn't then he could still do anything else arc energy's used for. Spawning in enemy territories is dangerous since everyone resists electricity, a lot of things have pretty nasty powers, and he could take a wrong turn and end up obliterated by some random 5-C
Knight (Destiny).
Warhammer 40,000: Not a nice verse to be. Best case scenario is probably being similar to a sanctioned psyker, but I think it's far more likely that his stuff would result in him being executed if he's in the imperium. Spawning in Dark Eldar or Chaos territory is just bad, Orks is a constant fight until he dies, Tau's either indoctrination or (eventual) death, and the Eldar have already planned for his arrival and have a million things they could do with him depending on their aims.
Salt and Sanctuary: Probably is stuck on the island since stuff eventually gets too strong and the good ending has you swim out of it (which cole can't do), if we assume he's there. Otherwise he just lives a normal life.
Hotline Miami: I wonder if it's possible that he could put a damper on the cold war here and avert the ending of HLM2? If a nuclear war starts he still dies. Not immediately or to the radiation, but to starvation. He'd have some time to walk around in a dead or dying world, and would eventually succumb himself. Nuclear War's not a nice concept.
Hollow Knight: Lives a normal live, since he's too big to fit into underground caverns inhabited by bugs so he must just spawn in a regular area.
Super Smash Bros.…
The Legend of Zelda: Each game's generally a new setting so yeah I don't know
DOOM: Infinite electricity seems like a good solution to the energy crisis that necessitated conquering Hell for resources. He can kill demons and shit sure, but I feel like that would be a much more useful role to fill in especially since Doomguy seems to be doing fine with the demon killing.
The Cosmere: Lot of different settings, fits in to some magic systems better than others. Unusually powerful for sure no matter where he ends up.
Xionic Madness: Cole vs some weird government conspiracy but he's too durable to damage I guess. Though I'd assume they could requisition chemical weapons in some form and stuff like
XV is around, he would make the tasks of the protagonists a lot easier via 1 shotting everything and being invincible.
Devil Daggers: Cole just kills a bunch of skulls forever since that's all the verse is, it doesn't have a story lol
Titanfall (Verse): People would try and get him roped up into some war or another, and I doubt he'd have any of it. Would not be allowed into the Apex Games though, too powerful
Katana ZERO: I have no clue. Depending where he's at he might not even be privy to the whole shadow war going on.
Parahumans (Verse): Cauldron (and Dinah) already foresaw his arrival and made plans for him. He rises up to become one of the greatest heroes, maneuvered by background forces to help drive off the endbringers and destroy threats like the Slaughterhouse 9. Already has demonstrated control good enough to be non lethal against normal people, durability is a big plus, Cole could do really well as a hero here, though he probably wouldn't become Triumverate because they're all backed by Cauldron.
Contessa could figure out the right things to say to him to get him into the organization if needed though. Probably dies in the eventual fight against
Scion (Worm) because Scion kills >10 billion people and can just shut off his powers, but if he survives into ward he still mantains an important position being probably the most powerful human sans
Valkyre and maybe Goddess and an actual hero. Anti parahuman sentiment is much higher in Ward, but he is too durable to die in terrorist attacks or whatever and is genuinely heroic without the problems some other heroes in this verse have. Definitely would become a key member of the Wardens.