Mac Studio display turns off and on

Have you updated your Mac to the latest software version? I also had a flickering screen on sequoia 15.0 on my iMac, after the update to 15.1 it is gone

If not you can try to boot in the safe mode to see if the issue persist there. If the issue does not persist in the safe mode it is most likely caused by an external piece of software, you might want to evaluate the external software installed to your Mac

The very highest resolutions of the Apple Studio display demand a ThunderBolt cable that is remarkably SHORT. Apple highly engineered cable can be up to 0.8 meters, Brand-X cables must be 0.5 meters of shorter. ThunderBolt trademark must be marked on the cable to assure it is certified.

I also have this problem. The apple call centre guy had me setup a different login which did seem to help but it started again. everyone's at a loss as well. I had connected an external hard drive and I notice that when the screen goes off and on I get the "Eject before disconnecting" warning, so it does seem that the power somehow drops. also when it comes back on the screen colour seems to reset even after having turned off all the auto adjustments in settings. It'll have to go back to apple which is a mission but I think thats all thats left.

What model-year Mac studio and what processor?

can you get to Recovery? all maintenance modes go through Recovery on theses models.

I posted above about cable lengths. how long are your cables?