[BUG] /model picker omits Fable 5.1 on personal Max 5x account (non-org) despite entitlement

Preflight Checklist

• [x] I have searched existing issues (related: #91852, #92300)
• [x] This is a single bug report
• [x] I am using the latest version of Claude Code

What's Wrong?

The /model picker does not list Fable 5.1, even though the account is entitled to it.
Directly invoking the model works without error:

/model claude-fable-5-1
→ Set model to Fable 5.1 and saved as your default for new sessions

Only the picker's list is affected — the model itself is accessible. This matches #91852, confirmed with an identical cache signature, but on a personal (non-Enterprise, non-Team) Max 5x subscription with no managed settings — so the bug isn't specific to org/managed-settings configurations.

Steps to Reproduce

1. Authenticate on a personal Claude Max 5x account via claude.ai OAuth (no Enterprise/Team org)
2. Run claude --version → confirm 2.1.273
3. Run /model inside a session
4. Observe: only "Fable" (5) is listed; Fable 5.1 is absent
5. Run /model claude-fable-5-1 directly → succeeds and sets as default

Expected Behavior

/model should list Fable 5.1 alongside Fable 5 for any entitled account, matching what direct invocation already allows.

Environment

• Platform: macOS 27.0 (26A428)
• Terminal: tmux 3.7b inside otty 1.4.1 (xterm-256color)
• Claude Code version: 2.1.273
• Plan: Claude Max 5x, personal subscription (billingType: stripe_subscription); no Enterprise/Team org, no managed-settings.json (/Library/Application Support/ClaudeAgent/ absent)
• Auth method: claude.ai OAuth

Additional Context

~/.claude.json cache state — identical pattern to #91852:

"additionalModelOptionsCache": [
  {
    "value": "claude-fable-5[1m]",
    "label": "Fable",
    "description": "Fable 5 · Most capable for your hardest and longest-running tasks"
  }
],
"modelAccessCache": [],
"orgModelDefaultCache": null

modelAccessCache is empty and additionalModelOptionsCache has only the Fable 5 [1m] variant — no Fable 5.1 entry is ever written to this cache, yet direct model selection succeeds. The picker appears to read from this cache while direct /model <id> bypasses it, which points at cache population rather than entitlement. Confirms this is not org-specific: reproduces on a plain personal Max 5x account with no managed settings.

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