[codex] Add externally provided Codex auth (#31274)

## Summary

Add an in-memory externally provided Codex auth snapshot with explicit
runtime capabilities, installed through the existing `ExternalAuth`
provider path.

## Testing

- `just fmt-check`
- `cargo test -p codex-login --lib externally_provided_auth`
- `cargo test -p codex-core --lib
external_auth_snapshot_is_installed_from_runtime_config`
- `cargo test -p codex-model-provider --lib external_auth`
- `cargo test -p codex-mcp-extension --test hosted_apps_mcp
hosted_apps_mcp_accepts_external_provided_codex_auth`
- `cargo check -p codex-app-server -p codex-core-api -p
codex-thread-manager-sample`

---------

Co-authored-by: pakrym-oai <pakrym@openai.com>

codex-rs/cli/src/doctor.rs

@@ -1327,6 +1327,7 @@ fn stored_auth_mode(auth: &codex_login::AuthDotJson) -> &'static str {
         AuthMode::ApiKey => "api_key",
         AuthMode::Chatgpt => "chatgpt",
         AuthMode::ChatgptAuthTokens => "chatgpt_auth_tokens",
+        AuthMode::Headers => "headers",
         AuthMode::AgentIdentity => "agent_identity",
         AuthMode::PersonalAccessToken => "personal_access_token",
         AuthMode::BedrockApiKey => "bedrock_api_key",
@@ -1397,6 +1398,9 @@ fn stored_auth_issues(
                 issues.push("external ChatGPT auth is missing refresh metadata");
             }
         }
+        AuthMode::Headers => {
+            issues.push("header auth cannot be loaded from auth storage");
+        }
         AuthMode::AgentIdentity => {
             if auth
                 .agent_identity
@@ -2466,6 +2470,7 @@ fn auth_mode_name(auth: &CodexAuth) -> &'static str {
         AuthMode::ApiKey => "api_key",
         AuthMode::Chatgpt => "chatgpt",
         AuthMode::ChatgptAuthTokens => "chatgpt_auth_tokens",
+        AuthMode::Headers => "headers",
         AuthMode::AgentIdentity => "agent_identity",
         AuthMode::PersonalAccessToken => "personal_access_token",
         AuthMode::BedrockApiKey => "bedrock_api_key",
@@ -2605,6 +2610,7 @@ fn provider_auth_reachability_mode_from_auth(
         Some(
             AuthMode::Chatgpt
             | AuthMode::ChatgptAuthTokens
+            | AuthMode::Headers
             | AuthMode::AgentIdentity
             | AuthMode::PersonalAccessToken,
         )