The strip now owns a single dropdown per tab, fed by the header with
items bound to that tab's session — rename (activates the tab first),
copy id, share/copy link/unshare, export and move-to-worktree (active
tab only, they need the loaded directory), close other tabs, archive
and delete with the confirm dialog targeting the right session. The
separate inactive-tab menu is gone, and there is no Close item — the
tab's close button covers it, now placed after the menu button.
Right-click opens that menu without activating the tab. The menu's
anchor overlay stays mounted until the close animation finishes, which
removes the popup flashing in the top-left corner on close. The
scroller hides its scrollbar via a dedicated CSS class (the bar was
shifting the header content vertically).