Claude models missing from Agents window model picker in 1.136 (regression from 1.135)

Does this issue occur when all extensions are disabled?: Not tested — I'm not certain
whether I tried this specifically during the affected window.

- VS Code Version: 1.136.2 (regression from 1.135, which worked correctly)
- OS Version: macOS, Apple Silicon (Darwin arm64 25.6.0)

Steps to Reproduce:
1. Open the Agents window in VS Code 1.136.2 and select "Claude" as the agent — the
model picker shows "No models available." GitHub Copilot and Codex both work
normally in the same Agents window at the same time.
2. Open "Manage Language Model Access" — only "GitHub Copilot" is listed as a
provider; there is no Anthropic/Claude entry.
3. Downgrade to VS Code 1.135 with no other changes — Claude models reappear
immediately in the same Agents window.

Expected behavior: Claude models should remain available in the Agents window via
the existing Anthropic account/subscription (OAuth), consistent with 1.135 behavior.

Additional context:
- Auth method is an Anthropic subscription via OAuth — not an API key, and not
routed through GitHub Copilot billing.
- The Claude Code extension continues to work normally in the main editor window
throughout, so the extension and its credentials are functioning correctly —
the issue appears specific to the Agents window's model registration for Claude
on 1.136.
- Troubleshooting attempted on 1.136 before downgrading (in no particular order,
and I may not have full recall of everything tried): restarted VS Code multiple
times; enabled chat.agentHost.allowSignedOutWhenUsable (no effect — this setting
is for users not signed into GitHub, which doesn't apply here since GitHub is
signed in); signed out and back in to my GitHub account in VS Code; disabled and
re-enabled the Claude Code extension; checked the Output panel for Claude/Agent-
related log channels. None of these restored Claude models on 1.136.
- Related: anthropics/claude-code#68809