No. There is no way to get MacOS to be able to switch between open windows on a desktop via a keyboard shortcut without installing 3rd party software that adds this basic functionality.
Cmd-tab, and then while holding command, use up/down arrow to drill into the windows for a specific app. I realize that this is not great if you need to switch back and forth between the same two windows over and over again.
Nope, that doesn't do it. If I have 2 Chrome windows and 3 terminal windows and 2 text editor windows open on MacOS, there is no way to merely switch from a Chrome window to a specific terminal window. You have to switch to the terminal application, which raises all 3 terminal windows to the top of the window stack on whichever display they are on, then switch between terminal windows. To enable the basic feature of switching directly between windows, you have to install 3rd party software.
I get with keyboard only to a specific window without any 3rd party app this way... I think the question is solved in a way (not saying it's the best way)