In the end, I have decided against a 3080. It's impossible to get one at a reasonable price that I'm willing to pay. I went with a 3070 instead, which has been shipped this morning.
If everything works out, it should arrive by the end of the week. In the first step, I'll upgrade my current gaming-PC and replace the 1080 with the 3070. Then I'll slowly get the remaining gear to do a full upgrade.
I have to admit I am more excited than I should be. Finally being able to play Cyberpunk at something higher than the lowest settings. Finally being able to play Skyrim (yes, Skyrim! The modlist I use has crazy mods and a crazy ENB installed) at max resolution. Yes, I'm still hyped for a nearly ten-year-old game.