Modal surfaces never mark #root aria-hidden — background stays in the a11y tree

[HomenShum]

Found during the Radix primitive migration before/after probe (PR #209,
evidence in docs/design/ui-contract/20260717-radix-primitives/README.md).

Problem: while the command palette (and by extension other modal dialogs) is
open, #root is never marked aria-hidden, so all background app content stays
reachable in the accessibility tree. This is true on BOTH sides of the migration:

• pre-Radix: dialog rendered inline inside #root with aria-modal="true" — but
  aria-modal alone does not prune the tree (measured: aria snapshot GREW 185→202
  lines with the modal open).
• post-Radix: dialog is portaled to document.body with focus guards, aria-modal
  dropped (Radix relies on hideOthers), but hideOthers is not marking #root
aria-hidden (measured: #root aria-hidden stays null while open).

The observed 185→49 aria-snapshot shrink post-Radix is most plausibly scroll-lock
unmounting virtualized binder rows, NOT aria-hiding — do not count it as the fix.

Definition of done: with any shared-primitive modal open, #root (or every
body-level sibling of the portal) carries aria-hidden="true"/inert, verified by
a Playwright assertion added to the primitive suite, not by manual inspection.

Suspects to check first: whether react-remove-scroll/aria-hidden package is
present and why hideOthers skips #root; whether a custom DialogPortal container
breaks Radix's sibling-hiding walk.

[HomenShum]

Root cause found and fixed in commit 942bb35 (lands with the next push) — it differs from this issue's original hypothesis.

What was actually happening: Radix's `hideOthers` was working correctly. The `aria-hidden` package exempts every `[aria-live]` element AND its entire ancestor chain from modal hiding (screen-reader announcements must survive modals). Three explicit `aria-live` attributes on real UI pinned large background subtrees open behind dialogs:

1. `button.r-roomcode` (invite chip) — pinned the topbar chain
2. `div.r-chat` (the whole 130-element chat feed) — pinned the chat rail
3. `div.r-status-strip` — pinned the footer strip

Fix: invite-copy announcement moved to a dedicated visually-hidden `LiveRegion` leaf; chat feed uses `role="log"` (implicit polite liveness, additions-only — better SR behavior anyway); status strip / offline pill rely on `role="status"` implicit liveness.

Measured (aria snapshot lines with command palette open): 202 (pre-Radix, aria-modal era) → 49 (post-Radix, live-region pins) → 20 (dialog-only, zero background leak).

Guarded by `e2e/modal-aria-hiding.spec.ts`, which pins: background controls carry `data-aria-hidden` while the modal is open, the only live exemption inside #root is an empty announcement leaf, and dismissal restores the tree.