refactor: route Codex auth through AuthProvider (#18811)

## Summary

This PR moves Codex backend request authentication from direct
bearer-token handling to `AuthProvider`.

The new `codex-auth-provider` crate defines the shared request-auth
trait. `CodexAuth::provider()` returns a provider that can apply all
headers needed for the selected auth mode.

This lets ChatGPT token auth and AgentIdentity auth share the same
callsite path:
- ChatGPT token auth applies bearer auth plus account/FedRAMP headers
where needed.
- AgentIdentity auth applies AgentAssertion plus account/FedRAMP headers
where needed.

Reference old stack: https://github.com/openai/codex/pull/17387/changes

## Callsite Migration

| Area | Change |
| --- | --- |
| backend-client | accepts an `AuthProvider` instead of a raw
token/header |
| chatgpt client/connectors | applies auth through
`CodexAuth::provider()` |
| cloud tasks | keeps Codex-backend gating, applies auth through
provider |
| cloud requirements | uses Codex-backend auth checks and provider
headers |
| app-server remote control | applies provider headers for backend calls
|
| MCP Apps/connectors | gates on `uses_codex_backend()` and keys caches
from generic account getters |
| model refresh | treats AgentIdentity as Codex-backend auth |
| OpenAI file upload path | rejects non-Codex-backend auth before
applying headers |
| core client setup | keeps model-provider auth flow and allows
AgentIdentity through provider-backed OpenAI auth |

## Stack

1. https://github.com/openai/codex/pull/18757: full revert
2. https://github.com/openai/codex/pull/18871: isolated Agent Identity
crate
3. https://github.com/openai/codex/pull/18785: explicit AgentIdentity
auth mode and startup task allocation
4. This PR: migrate Codex backend auth callsites through AuthProvider
5. https://github.com/openai/codex/pull/18904: accept AgentIdentity JWTs
and load `CODEX_AGENT_IDENTITY`

## Testing

Tests: targeted Rust checks, cargo-shear, Bazel lock check, and CI.

codex-rs/Cargo.lock

@@ -1773,6 +1773,7 @@ dependencies = [
  "codex-app-server-protocol",
  "codex-git-utils",
  "codex-login",
+ "codex-model-provider",
  "codex-plugin",
  "codex-protocol",
  "codex-utils-absolute-path",
@@ -1840,6 +1841,7 @@ dependencies = [
  "chrono",
  "clap",
  "codex-analytics",
+ "codex-api",
  "codex-app-server-protocol",
  "codex-arg0",
  "codex-backend-client",
@@ -1856,6 +1858,7 @@ dependencies = [
  "codex-git-utils",
  "codex-login",
  "codex-mcp",
+ "codex-model-provider",
  "codex-model-provider-info",
  "codex-models-manager",
  "codex-otel",
@@ -2045,9 +2048,11 @@ name = "codex-backend-client"
 version = "0.0.0"
 dependencies = [
  "anyhow",
+ "codex-api",
  "codex-backend-openapi-models",
  "codex-client",
  "codex-login",
+ "codex-model-provider",
  "codex-protocol",
  "pretty_assertions",
  "reqwest",
@@ -2071,11 +2076,11 @@ dependencies = [
  "anyhow",
  "clap",
  "codex-app-server-protocol",
- "codex-config",
  "codex-connectors",
  "codex-core",
  "codex-git-utils",
  "codex-login",
+ "codex-model-provider",
  "codex-utils-cargo-bin",
  "codex-utils-cli",
  "pretty_assertions",
@@ -2203,7 +2208,6 @@ version = "0.0.0"
 dependencies = [
  "anyhow",
  "async-trait",
- "base64 0.22.1",
  "chrono",
  "clap",
  "codex-client",
@@ -2212,6 +2216,7 @@ dependencies = [
  "codex-core",
  "codex-git-utils",
  "codex-login",
+ "codex-model-provider",
  "codex-tui",
  "codex-utils-cli",
  "crossterm",
@@ -2236,6 +2241,7 @@ dependencies = [
  "anyhow",
  "async-trait",
  "chrono",
+ "codex-api",
  "codex-backend-client",
  "codex-git-utils",
  "serde",
@@ -2460,6 +2466,7 @@ dependencies = [
  "codex-exec-server",
  "codex-git-utils",
  "codex-login",
+ "codex-model-provider",
  "codex-otel",
  "codex-plugin",
  "codex-protocol",
@@ -2491,6 +2498,7 @@ dependencies = [
  "codex-config",
  "codex-exec-server",
  "codex-login",
+ "codex-model-provider",
  "codex-otel",
  "codex-protocol",
  "codex-skills",
@@ -2849,10 +2857,12 @@ version = "0.0.0"
 dependencies = [
  "anyhow",
  "async-channel",
+ "codex-api",
  "codex-async-utils",
  "codex-config",
  "codex-exec-server",
  "codex-login",
+ "codex-model-provider",
  "codex-otel",
  "codex-plugin",
  "codex-protocol",
@@ -2912,6 +2922,7 @@ name = "codex-model-provider"
 version = "0.0.0"
 dependencies = [
  "async-trait",
+ "codex-agent-identity",
  "codex-api",
  "codex-aws-auth",
  "codex-client",
@@ -3154,6 +3165,7 @@ dependencies = [
  "anyhow",
  "axum",
  "bytes",
+ "codex-api",
  "codex-client",
  "codex-config",
  "codex-exec-server",