fix(web-plugin-config): address review — one options snapshot per search, no public value exports

Three findings from review survived against the staged-save head:

The search provider read its options thunk per property, so a settings write
landing inside credential resolution sent the key resolved from the old
section to the endpoint named by the new one. Each operation now snapshots
once at its entry and threads that snapshot into credential resolution; a
regression test drives a commit into the middle of a search and pins that the
endpoint, model, and key all come from the section the search started on.

The /client entry exported components, controllers, and namespace constants
with no consumer, which the client export discipline allows only with sign-off.
Only types remain. The duplicate per-card Injected/Face interface pairs are
one declaration each now, so a member added to one side cannot silently miss
the other.

The credential state carries the reference it describes and its writability: a
reference change no longer projects the old answer onto the new name, an
out-of-order response for a stale reference is dropped, and a key that a
deployment sources from the process environment disables the control instead
of inviting a write the Host must refuse.

Also corrected three prose claims against the code they describe: the card's
fields do not differ by platform (the served schema does), the section's empty
line counts registered rather than visible cards and is read once, and the
search README overstated what a configuration surface learns about a key.

packages/client/ui-plugin-config/README.md

@@ -34,4 +34,5 @@ None; this package neither assembles nor sends a provider request.
 
 - **Only host-plane plugins appear** — a plugin an agent preset mounts carries its configuration inline in that preset's `agent.cordis.yml` and cannot register a settings namespace at all (a second session mounting the same preset would fail on a duplicate registration), so this section lists nothing for it. Editing those values remains the preset editor's job.
 - **Exposure is a Host allowlist, not a plugin declaration** — a namespace absent from the api-proxy's allowlist answers `settings-not-exposed` even when its owner registered it, so a plugin distributed outside this repository cannot surface its own configuration here without a change in `packages/host/apiproxy`.
-- **The shell card follows the composed executor** — the POSIX and PowerShell executor families share the `bash` namespace because a host composes exactly one of them, so the card's fields differ by platform and a deployment composing neither shows no card.
+- **The shell card follows the composed executor** — the POSIX and PowerShell executor families share the `bash` namespace because a host composes exactly one of them, so the served schema differs by platform (PowerShell adds `pwshPath`) even though the card edits the same two fields on both, and a deployment composing neither shows no card.
+- **The empty line counts registered cards, not visible ones** — a card whose namespace this deployment does not expose renders nothing, but still counts, so a deployment that exposes none shows an empty list rather than the empty line. The count is also read once, because the renderer caches a root entry's inject face; a card registered later does not raise it.