After some frustration with shifted windows, usually even after a short break and monitor standby, I tried several solutions. Even tools that promised to save the fixed position were not satisfactory. My preferred go-to solution is now to define sets of window positions in a script for different work situations and simply call them up via keyboard shortcut. No third party tools needed, just works with AppleScript. The nice thing is, that it even works with multiple windows of the same app.

Here an example of my "Dev1" setting with three displays (two 27" external 4K displays and one 14" MacBook). Move Firefox to the first display and leave 50 pixel space for the left side dock. Move IntelliJ IDEA to the second and iTerm2 to the MacBook screen. Works reliable.

  use application "System Events"
  
  get (every window of process "firefox" whose value of attribute "AXMinimized" is false)
  repeat with W in the result
   set position of W to {50, 0}
   set size of W to {1870, 1080}
  end repeat

  get (every window of process "idea" whose value of attribute "AXMinimized" is false)
  repeat with W in the result
   set position of W to {1920, 0}
   set size of W to {1920, 1080}
  end repeat
  
  get (every window of process "iTerm2" whose value of attribute "AXMinimized" is false)
  repeat with W in the result
   set position of W to {1125, 1100}
   set size of W to {1510, 940}
  end repeat