## Context

Plugins can expose more than one way for Codex to use them: App
connectors for ChatGPT/SIWC-backed sessions and MCP servers for API key
login sessions. The broader goal is to make `PluginsManager` the place
that understands which plugin surfaces should be visible for the current
auth route, so callers do not each have to make that decision
themselves.

This PR is the small setup step for that work. It lets the plugin
manager be created with the current `AuthMode`, which gives the followup
auth routing PRs the information they need without relying on setter
injection.

## Stack

- PR1: #27652 seed plugin manager auth at construction.
- PR2: #27459 route plugin surfaces by auth mode.
- PR3: #27607 dedupe plugin MCP servers by App declaration name.
- PR4: #27602 preserve plugin Apps in connector listings.
- PR5: #27461 skip install-time plugin MCP OAuth for matching App
routes.

## Summary

- Let `PluginsManager::new_with_restriction_product` accept an initial
`AuthMode`.
- Keep `PluginsManager::new` behavior unchanged for ordinary callers.

## Validation

```bash
cargo test -p codex-core-plugins plugins_manager_tracks_auth_mode
cargo test -p codex-core list_tool_suggest_discoverable_plugins
git diff --check
```

---------

Co-authored-by: Xin Lin <xl@openai.com>

## Context

Some plugins expose both Apps and MCP servers. This PR moves auth-aware
surface projection into `core-plugins::PluginsManager`, so callers get a
consistent effective plugin view. Later PRs narrow the conflict rule and
update listing/install paths.

The high level goal of this PR is to set up the plumbing to
conditionally filter App/MCP in the plugin manager layer. We start by
removing MCP servers when using SIWC/Codex-backend auth, and removing
Apps when using API-key-style auth.

This PR is now stacked on #27652, which contains only the constructor
plumbing for seeding `PluginsManager` with the current auth mode.

## Stack

- PR1: #27652 seed plugin manager auth at construction.
- PR2: #27459 route plugin surfaces by auth mode.
- PR3: #27607 dedupe plugin MCP servers by App declaration name.
- PR4: #27602 preserve plugin Apps in connector listings.
- PR5: #27461 skip install-time plugin MCP OAuth for matching App
routes.

## Summary

- API-key/non-ChatGPT routes hide plugin Apps and keep plugin MCPs.
- ChatGPT/SIWC with Apps enabled keeps plugin Apps and suppresses MCPs
for dual-surface plugins.
- MCP-only plugins stay available for ChatGPT/SIWC sessions.
- Cached plugin load outcomes are re-projected when auth mode changes.

## Validation

```bash
cargo test -p codex-core-plugins plugin_auth_projection
cargo test -p codex-core list_tool_suggest_discoverable_plugins
git diff --check
```

## Context

This is the next step in the plugin auth-routing stack. The earlier PRs
make `PluginsManager` auth-aware and move the broad App/MCP surface
decision into that layer. This PR narrows the ChatGPT/SIWC behavior so
we only hide a plugin MCP server when it conflicts with an App
declaration of the same name.

In product terms: if a plugin exposes both an App route and MCP route
for `foo`, ChatGPT/SIWC sessions should use the App route for `foo`. If
the same plugin also exposes a separate MCP server like `foo2`, that MCP
server should remain available.

```json
// .app.json
{
  "apps": {
    "foo": {
      "id": "connector_abc"
    }
  }
}
```

```json
// .mcp.json
{
  "mcpServers": {
    "foo": {
      "url": "https://mcp.foo.com/mcp"
    },
    "foo2": {
      "url": "https://mcp.foo2.com/mcp"
    }
  }
}
```

## Stack

- PR1: #27652 seed plugin manager auth at construction.
- PR2: #27459 route plugin surfaces by auth mode.
- PR3: #27607 dedupe plugin MCP servers by App declaration name.
- PR4: #27602 preserve plugin Apps in connector listings.
- PR5: #27461 skip install-time plugin MCP OAuth for matching App
routes.

## Summary

- Preserve App declaration names in loaded plugin metadata.
- Keep public effective App outputs as deduped connector IDs for
existing callers.
- For ChatGPT/SIWC, suppress only plugin MCP servers whose names match
declared App names.

## Validation

```bash
cargo fmt --all
cargo test -p codex-core-plugins plugin_auth_projection
cargo test -p codex-core-plugins effective_apps
cargo test -p codex-core-plugins read_plugin_for_config_installed_git_source_reads_from_cache_without_cloning
cargo test -p codex-core explicit_plugin_mentions_use_apps_for_chatgpt_dual_surface_plugins
cargo test -p codex-core explicit_plugin_mentions_keep_non_conflicting_mcp_for_chatgpt_auth
cargo test -p codex-app-server --test all plugin_install_filters_disallowed_apps_needing_auth
git diff --check
```

---------

Co-authored-by: Xin Lin <xl@openai.com>