Show activity for standalone web search calls (#24693)

## Why

Standalone `web.run` calls run in the extension, so they need normal
web-search progress activity while a request is in flight and durable
completed activity after a thread is reloaded.

Follow-up to #23823; uses the extension turn-item emission path added in
#24813.

## What changed

- Emit standalone `web.run` start/completion items through the host
turn-item emitter, preserving standard client delivery and rollout
persistence.
- Include useful completion detail for queries, image queries, and
literal-URL `open`/`find` commands.
- Render completed searches as `Searched the web` or `Searched the web
for <detail>`, with snapshot coverage for the detail-free case.
- Extend the app-server round-trip test to verify completed search
activity is reconstructed by `thread/read` after a fresh-process reload.

## Testing

- `just test -p codex-web-search-extension`
- `just test -p codex-app-server -E
"test(standalone_web_search_round_trips_encrypted_output)"`

codex-rs/Cargo.lock

@@ -4174,6 +4174,7 @@ dependencies = [
  "pretty_assertions",
  "schemars 0.8.22",
  "serde_json",
+ "url",
 ]
 
 [[package]]