Unfortunately I cannot provide a solution. I used to have a similar problem with an FP2 running LineageOS (16 or 17, I think). However, to be precise, the FP2 display would turn to very low brightness when “it was time” for sleep mode which I think we both would expect to be all black. Strangely, this problem disappeared through an update, upgrade or switch to a different OS at one point (I think in 2021 or even 2020) and it has not returned when I recently upgraded the device from Fairphone Open Android 9 to Fairphone Open Android 10.
Additional info (remembering it only now): I think the issue only occured when the phone was charging.
Others more knowledgeable than me: Might modem.zip be a suspect? If yes, how could Tuvok update this? (I was last told about how to some years ago when Fairphone OS still ran with TWRP as recovery)
P.S.: Found a topic where I previously reported my observation, see first link in lines 1 and 2.