muxg: migrate the legacy session picker to the shared popover path

open   by a73x

After a separately shipped and reviewable shared popover core plus recovery/force-End consumer, migrate the legacy session picker.

Scope: preserve picker discovery/attachment semantics while replacing only its duplicated presentation/input path; do not combine with S1 core simplification or recovery/End completion.

Acceptance: legacy picker/empty-workspace behavior remains covered, no workflow policy enters the window-free model, native GUI gates and independent review pass.