The Gateway item is the only statusbar entry with variant === 'menu'.
Since da73223f4 wrapped every render branch in `Tip`, the menu branch
nested `<DropdownMenu>` (a Radix Root that renders no DOM node) inside
`Tip`'s `<TooltipTrigger asChild>`. With no element to attach to, Radix
could never wire hover listeners, so the tooltip silently never showed.
`Tip` also can't be moved inside `DropdownMenuTrigger asChild` (the shape
proposed in #54859): it's a plain component, not a Slot-forwarding one, so
the trigger's injected ref/handlers would land on `TooltipContent` instead
of the button and break the menu's click + popper anchoring.
Fix by composing both trigger Slots directly onto a single <button>
(`TooltipTrigger asChild` over `DropdownMenuTrigger asChild`), the pattern
already used in profile-switcher.tsx, and skip the tooltip wrapper entirely
when the item has no title.
Supersedes #54859.
Co-authored-by: wnuuee1 <wnuuee1@users.noreply.github.com>
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