Anecdotal, but I spent years not sleeping through university and sleeping in airports or on the train. Studied engineering and did a lot of hackathons and events and stuff. I figured out then that I didn't need full cognition or excellent decision making. I needed more hours cranking out work. I spent years sleeping just a few hours and often not sleeping on Saturday at all.
I do a lot less of that now as work never has 2AM deadlines but it is as though I am permanently in that 80% functionality state. I never felt that I got out of that state. I have never regained my ability to be detail oriented. I am still reliant on the crutches of spell check and Grammarly and my IDE to make sure I don't do something stupid. I use task lists for every little thing in my day.
So it is not that it does not impact cognition (at least in my case), it is that you get used to that impaired state and can't find a way back.
Only a year and a half removed from that, so maybe it takes more time, but I still feel heavily optimized for output over quality, even though that is no longer needed.
My baseline cognition was already impacted. More sleep just did not repair it.