As shared in the prior thread, you could rule out a number of things and just possibly find a solution if you would test a wired (ethernet) connection. I know you want to use wifi only but a test is just a test. One cable from router to AppleTV (right across the floor if need be for this test) to see if it works well that way would rule out key possibilities that it is something other than "crappy" satt broadband. For example, what if the upped satt service IS fast/stable enough but the wifi functionality of your router is failing (not quite dead but on its way out)?
One easy run of an ethernet cable would bypass wifi variables completely to see if the satt service is good enough. If so, a simple router change may yield a better wifi connection and you get what you were hoping for without simply doing without until a non-satt, broadband option may arrive. Those kind of projects seem to take 2X-5X longer than best estimated, so taking one more shot at getting your "as is" working may be worth this (simple) test effort.
If AppleTV suddenly works well via ethernet, router replacement becomes next step to freshly test wifi again. If that "fixes" it for AppleTV, HomePods are likely to work better too. On the other hand, if AppleTV continues to NOT work well with a wired connection test, fault is very likely with the satt service- presumably too many interruptions in data flow- and your next best bet does become changing source of broadband.
If you picked up the AppleTV without an ethernet jack, you can test this with ANY device (maybe a laptop?) with an ethernet jack. Position the laptop where you keep your AppleTV, do some speed tests over wifi (speediest.net or similar), direct connect with ethernet, repeat those tests, compare results. If it is noticeably better with ethernet, I again suspect failing router and that is a simple change that might make a huge difference.
