Button drawn in the parent window over the ##chat2-messages child was never
clickable: ImGui resolves g.HoveredWindow to the child for that screen rect, so
ItemHoverable rejects any item submitted in the parent. A top-level Begin/End
window is a sibling in the window list and wins the hit-test for its own rect.
ownerId parameter keeps the window name distinct between the main window and
each pop-out, preventing Begin/End collisions when both render in the same frame.