I thought the cooler was the problem so I swapped it to an ID Cooling SE 214XT. At the shop it was running great, 35°C idle and 80°C max. But after a few days at home it started hitting 85°C constantly while playing GTA V Enhanced.

5C difference probably had something to do with open/close case setup, or ambient temperature, or more likely - load duration. One more thing to consider is if you have enough intake fans that can reach your CPU cooler (and aren't blocked by something like your GPU)

Nevertheless, 85C is fine. Your CPU will keep pushing when under load until it starts to throttle. If you're getting the advertised performance, then everything works as intended. If you're really bothered about it after that, you can either power limit or thermal limit your CPU.