Stacked on #22448.
This moves the broader follow-up behavior out of the parent PR so the
parent stays focused on the `plugin/installed` mention-list API.
Changes:
- Start remote installed bundle sync from `plugin/installed`.
- Pass request-processor remote scopes into the bundle sync path.
- Include remote installed scopes in effective plugin load cache
handling.
- Keep the bundle sync coverage in this child PR instead of the parent.
Validation:
- `cargo check -p codex-core-plugins`
- `cargo check -p codex-app-server`
- `cargo test -p codex-core-plugins remote_installed_plugin`
- `env RUST_MIN_STACK=16777216 cargo test -p codex-app-server --test all
plugin_installed_`
- `just fix -p codex-core-plugins`
- `just fix -p codex-app-server`