I was wondering if you have a VGA cable and if it does the same? These are just my rambling thoughts BTW, as I'm no electronics expert!
If you look here:
https://info-coach.fr/atari/hardware/in ... itel_cable the SCART cable may have resistors installed that are not needed by the STE, but by using a VGA adapter you would eliminate this. If all is well using VGA you may have a problem with the SCART cable. Also, if you have a VGA switcher, you can also try using Hi Res and see if the problem still occurs.
If you have a simple composite cable you could also see what results that gives too, as it is the simplest video cable you can use.
If it occus at Low/Med & Hi Res, using SCART, VGA or Composite then it would seem like a video circuitry problem.
You seem to have confirmed it isn't PSU as you say you've used different PSUs, so that's also good.
Given your description, it almost seems like maybe it's capacitance related as it seems like there's a 'charging' time before the problem appears. This may not be a capacitor specifically, but a capacitance within the circuit (
@exxos correct me if I am wrong electronically here).
If you can, get a magnifying glass and check all the joints in the video circuitry for evidence of bad soldering/dry joints that need a reflow, and maybe also consider recapping the video circuitry.