Every other action — switching account, signing out of one, joining a
suggested or invited workspace — now resolves back into an open popover so
the result is visible where it happened. The swingset prototypes fake the
round trip they make against Clerk, so the spinner and stood-down rows are
demonstrable without a running app.

The sizes track the Icon scale (sm 14px, md 16px) so a spinner can stand in
for the icon it replaces, and the UserButton's trailing column is now one
slot the width of the menu button, so the spinner, the active check, and the
menu all sit on the same centre line.

The trigger carried the avatar alone. It now names what is active beside it — the
organization and its plan wherever one heads the trigger, the account otherwise —
behind `showLabel`, which defaults on.

Badge's `neutral` color was unreadable in both schemes: its fill is a 900 and its
text token is a text color, not an on-fill one. It now rides the same black/white
scrim the button's neutral fill does.

…ccount

The trigger and the popup's header now always name the same workspace. `combined`
carries both switchers, so `modePriority` picks which one it leads with: the active
organization by default, the account with `modePriority="user"`. Both are still listed
either way.

…onnected test

…ser fixture

The controller now reads hasOrganizations off the user resource, so the mocked user needs the field the real one has.

`setActive` swaps the active organization while its promise is still in
flight, so the popup rearranged mid-action: the header renamed itself, the
check jumped rows, and Invite came and went as the permission was re-read.
The connected component now snapshots the controller when an action starts
and renders that until it settles, so the result lands in one step.

Two smaller faults fell out of the same interaction:

- The spinner waited out a delay window before appearing, and the check
  raced ahead of it. Every action here is a network round trip, so there
  is nothing to debounce: `useSpinDelay` takes `delay: 0` and shows the
  value in the same pass, with `minDuration` still steadying it.

- A row going busy swapped its host element from `<button>` to `<div>`,
  remounting the subtree and dropping the avatar back to its initials for
  the length of the action. A row that stands down now stays the button it
  was, disabled, and `Avatar.Image` resolves a browser-cached `src` in a
  layout effect so neither a remount nor a swap flashes the fallback.

The popover stayed up behind the surface it opened. Managing, inviting, creating an
organization, and adding an account now close it on the way out, whether they open a modal
or navigate.

The connected test drives the real controller against a mocked Clerk, which is what
makes it worth having and also what makes it slow. Cases that only ever asserted what
the popover renders now sit in the view test, leaving the connected one to prove the
layers compose. Also covers `hidePersonal` reaching the popover through the container.

UserButtonProps picked only modePriority off the root, so the connected component was hard-wired to the combined surface and the orgs/user modes were reachable only by composing UserButtonView directly.

Presses a custom row on the connected UserButton and checks the app's
callback runs and the popover closes behind it.

An instance with organizations turned off has none to lead with or list,
so the button is the account's whatever `mode` asked for — `orgs` would
otherwise render an empty shell of a switcher. clerk-js withholds its own
OrganizationSwitcher at the mount boundary, which an app importing this
one never crosses, so the gate lives in the component.

The popover's open state and the one action in flight are the same flow, so
they now live in one machine instead of two useStates. Re-entry, clearing
busy, and closing on success stop being hand-written in the container: RUN is
simply unhandled while busy, and busy is only reachable from open.

Dismissing the popover mid-action now abandons the result rather than letting
it land in a surface that is already gone.

Follows the view's rename of `'orgs'` to `'organization'`.

Also corrects the integration suite's opening comment, which attributed
close-on-success to the container and had the navigation case backwards.