[BUG] Fable 5 gated behind "Requires usage credits" under CLAUDE_CODE_OAUTH_TOKEN auth — client discards subscriptionType it already has

### Preflight Checklist

- [x] I have searched existing issues and this hasn't been reported yet
- [x] This is a single bug report
- [x] I am using the latest version of Claude Code

### What's Wrong?

When Claude Code authenticates via the `CLAUDE_CODE_OAUTH_TOKEN` environment variable (e.g. a long-lived token from `claude setup-token`), the `/model` picker gates Fable 5 behind "· Requires usage credits" even though:

- the token belongs to a **Max 5x** account whose plan includes Fable 5,
- the same account on the same machine shows Fable as included when using normal keychain login (`claude auth login`),
- the API itself happily serves Fable to this exact token: `CLAUDE_CODE_OAUTH_TOKEN=... claude --model fable -p "hi"` works.

So the gating is purely client-side and contradicts both the account's actual entitlement and the server's behavior.

Root cause (from reading the 2.1.220 bundle): when the token comes from the env var, the credential object is built with the plan metadata hardcoded to null:

```js
if (env.CLAUDE_CODE_OAUTH_TOKEN) return {
accessToken: ..., refreshToken: null, expiresAt: null,
scopes: [...], // defaults to ["user:inference"]
subscriptionType: env.CLAUDE_CODE_SUBSCRIPTION_TYPE || null,
rateLimitTier: env.CLAUDE_CODE_RATE_LIMIT_TIER || null
};
```

`subscriptionType: null` then flows into the plan checks and the feature-flag user context (which omits `subscriptionType`/`rateLimitTier` when null), so the model picker treats the session as unknown-plan and falls into the credits-required branch — even though the cached `oauthAccount` in the config dir's `.claude.json` says `organizationType: "claude_max"` from a successful profile fetch. The client has the entitlement data; the picker just doesn't consult it in env-token mode.

Setting the (undocumented) overrides `CLAUDE_CODE_SUBSCRIPTION_TYPE=max` and `CLAUDE_CODE_RATE_LIMIT_TIER=default_claude_max_5x` fixes the picker, which confirms the mechanism.

### What Should Happen?

With `CLAUDE_CODE_OAUTH_TOKEN` auth, Claude Code should resolve the plan from the cached `oauthAccount` profile (or re-fetch it) instead of assuming "no plan", so Fable 5 shows as included for accounts whose plan includes it — matching what the server actually serves and what keychain login shows for the same account.

If env-token sessions are intentionally excluded from subscription model entitlements, the picker message should say that ("not available with long-lived token auth — run /login") rather than the misleading "Requires usage credits", and `CLAUDE_CODE_SUBSCRIPTION_TYPE` / `CLAUDE_CODE_RATE_LIMIT_TIER` should be documented.

### Error Messages/Logs

```shell
# /model picker entry under CLAUDE_CODE_OAUTH_TOKEN auth:
# Fable Fable 5 · Most capable for your hardest and longest-running tasks · Requires usage credits
# Same account via keychain login: no "Requires usage credits" suffix, Fable selectable.
```

### Steps to Reproduce

1. On a Max account, mint a long-lived token: `claude setup-token`.
2. In a fresh shell: `export CLAUDE_CODE_OAUTH_TOKEN=` (optionally a dedicated `CLAUDE_CONFIG_DIR` that has completed onboarding with this account).
3. Run `claude`, open `/model` → Fable 5 shows "· Requires usage credits" / selection is gated.
4. Exit; run `CLAUDE_CODE_OAUTH_TOKEN= claude --model fable -p "reply ok"` → succeeds, proving the token is entitled to Fable server-side.
5. Re-run step 3 with `CLAUDE_CODE_SUBSCRIPTION_TYPE=max CLAUDE_CODE_RATE_LIMIT_TIER=default_claude_max_5x` also exported → Fable shows as included.

Reproduced with two different accounts (Max 5x personal, Team with Fable) on the same machine; both are gated under env-token auth and fine under keychain login (CLI or macOS app).

### Claude Model

Other (Fable 5)

### Is this a regression?

I don't know

### Claude Code Version

2.1.220 (Claude Code)

### Platform

Anthropic API (claude.ai subscription auth)

### Operating System

macOS

### Terminal/Shell

Other (kitty)

### Additional Information

Related but distinct: #80749, #79337, #79341, #79576 all report Fable credits-gating under normal keychain login (intermittent / server-side flag causes). This report is deterministic and specific to `CLAUDE_CODE_OAUTH_TOKEN` auth: the client discards plan metadata it already has. Use case: running two subscriptions side by side via per-account long-lived tokens injected through the env var.

Start with the 2.1.220 bundle's CLAUDE_CODE_OAUTH_TOKEN credential construction and trace how subscriptionType reaches the /model picker and feature-flag user context. Inspect the cached oauthAccount in .claude.json and reproduce with the documented environment variables; done means an entitled Fable account is shown as included under token auth, or the picker gives an accurate limitation message.

Written by the indexing model from the issue text.