Moving between windows of the same app is cmd+~. Cmd-tab moves to another app, remaining on the same desktop if that has a window there.
The delay in focus can be reduced by turning off animations in “accessibility”.
Regardless, I’m with you on that everything is way more snappy on my Linux machine. Even if it’s running a “full” WM/DM like KDE.
The "All Applications" section lets you define global shortcuts. As long as there is a menu bar item for it (in this case, one from the Window menu) you can define a shortcut for it.