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vertico-posframe makes a pop-up in the middle of the screen for completion specifically. This is probably what you want.
There's also my package [hypop](https://github.com/mitchmarq42/hypop.el) which separates out the whole minibuffer and hides it when not in use. It has a few major drawbacks and only works on the hyprland desktop right now so probably don't use it.
I suggest you to reconsider if you really want a popup frame (posframe). One of the great features of Emacs in my opinion is that it does not by default create popup frames for user input like other programs. I suspect because of its origins as a terminal application. Don't you ever get frustrated by applications that have such popups which quite often appear on a different workspace! I'm not suggesting the posframe solutions others have suggested also suffer from this behaviour.
I'm not suggesting the posframe solutions others have suggested also suffer from this behaviour.
Then what was the point of the rest of the comment?
Posframes (child frames) always display on top of the root Emacs frame. Modal dialogs like menu-set-font are OS windows which do suffer from the problem you mentioned... except for the vast majority of systems where they just display on the right workspace by default.
When I wrote hypop, I specifically make it find the workspace Emacs is on to summon the minibuffer window to. It's really not that hard at a small scale.
Then what was the point of the rest of the comment?
I was giving my opinion on what I consider a great design choice of Emacs by not having such windows by default.