AnyPiP

AnyPiP takes the frontmost app window and keeps a picture-in-picture copy of it floating above your other windows. You start or stop it from the menu bar or a global shortcut, and a second shortcut returns the window to its normal place. Selected apps can switch into picture-in-picture automatically when they lose focus, and hovering over the floating copy takes you back to the source app. It suits anyone who follows a video, call or chat in one window while working in another.

It needs macOS 26.4 or later, plus Screen Recording permission for ScreenCaptureKit and Accessibility permission to move and focus source windows. The README is short and does not say whether the builds are notarized.