I've had the same thing, but only with 2 games. 1st was Deathloop, & more recently Elden Ring. For me it was definitely a temperature thing. I even complained to Sony while I was complaining about having to send the same dualsense back to them twice (R2, then L2 spring failures), after it had already been replaced by the shop once for stick drift. They replied regarding the controller & sent back a new replacement, but didn't even touch on me mentioning the console turning off.
Every time it did it with Deathloop, the back was red hot, & when it did come back on, the external hard drive would be corrupted, to the point it couldn't recover it, & I kept having to swap usb sockets until it would recognise the drive again. Finished Deathloop & traded it in straight away. Had to completely wipe the external drive, & re-install my PS4 Games. No problems with any other games, until Elden Ring. Don't play FIFA so no idea on that.
The most annoying thing is Elden Ring is a double wammy, the console gets hot, turns off, & then bitches at me that I didn't turn it off properly, complains that external HDD was disconnected, & then repairs it. Then the game bitches that I exited it without leaving the game properly. It's like the game & console are blaming me for not knowing the console is overheating.
I did end up sorting it though, took the covers off, took the fan out, cleaned the fan thoroughly, took the black cover off on the side the blu-ray drive is mounted in, & removed & as much of the dust out of the inside as I could physically get to through the hole where the fan was. I've done a complete strip down (motherboard out) on both a PS4 & a Pro, just to shut the noisy fans up, but didn't want to go that far with the PS5 yet. Once I'd cleaned what I could, I just kept blowing through every vent until dust stopped coming out (run out of compressed air, so good old lung power). Put it back together, & it's been fine since. The temperate on the back is nowhere near as hot, nor is it as concentrated in that one spot at the bottom. The heatsink vents that ran at the side of the fan were completely blocked. My PS5 is back in our open back TV cabinet, wedged between a PS3 slim & a Sky box (it's been sat on the floor next to the cabinet for a couple of months) & hasn't turned off since, & I've been playing a lot of Elden Ring.
Downside now is I've managed to crush the ribbon cable for the power light strip when putting the case back together, so no console lights at all. Ordered a new one from Ebay for £2.49, & the console still works fine, so no biggy.
Does annoy me that there's no warning before it turns off, & then the worry that will it actually come back on this time?
It's not great having to do this, & I think Sony have fobbed you off, but it wouldn't suprise me if it's dust that the air can just won't get rid off without taking the fan out. I'm not saying you should do it, but if you do, make sure you get a torx security screwdriver, the one with the hole in the end, T8 I think, as standard Torx don't work. It's not difficult, doesn't take that long, but you do have to peel off the warranty sticker on the black case for one of the screws. Make sure you check out a few PS5 teardown youtube videos. Oh, & be careful of that skinny little ribbon cable for the light strip.
Hope you manage to get it sorted.
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