Under the keyboard shortcuts this one is defaulting to Cmd+Backtick, and is known as "Move focus to next window".
When Stage Manager is active, the behavior of this thing changes from cycling windows in a given app, to cycling windows in a Stage Group. This is a desirable change that works well, but the glaring oversight here is not providing a fallback to allow the original behavior somehow. I am on Ventura and preferring not to upgrade to Sonoma yet.
The use case is as follows: You have one group with a safari window and textedit, and another group with the other safari window. Once you app-switch from some other group into safari, it will open whichever group you last used that has one of these Safari windows. From this point, it's impossible to use the keyboard to toggle to the OTHER safari window. One might reasonably argue that we have stage manager enabled so just switch your brain to stage manager mode, and yes I suppose I will explore the new actions for cycling stage manager groups, but that doesn't address the issue. This also kind of highlights another way in which stage manager is half-baked, as the app switcher should really completely change instead of being app centric to being group-centric. Which it has not. If we had this, this could be a reasonable resolution to the problem of not being able to switch to the other safari window without a multi stage mouse click interaction.
I'm curious if anyone knows a way to get back a way to trigger the original behavior of cycling app windows somehow. I think if we were to use applescript or some such to recreate the behavior the latency will be unacceptable. (that is how i drive cmd+backtick from alacritty which stubbornly refuses to implement proper window management. And it is laggy and has a huge problem with Stage Manager as well)