[BUG] claude.ai connectors show "Connected" but unusable across all Claude products

### Preflight Checklist

- [x] I have searched [existing issues](https://github.com/anthropics/claude-code/issues?q=is%3Aissue%20state%3Aopen%20label%3Abug) and this hasn't been reported yet
- [x] This is a single bug report (please file separate reports for different bugs)
- [x] I am using the latest version of Claude Code

### What's Wrong?

I have 4 claude.ai-hosted connectors (Supabase, Vercel, HubSpot, Canva), all showing Connected at claude.ai/customize/connectors.

None of them are actually usable, confirmed across three different Claude products:
- Claude Code (VS Code extension) — /mcp shows all 4 as "Needs Auth"
- claude.ai website (new chat) — same result
- Claude browser extension — same result

This rules out a session-caching issue. HubSpot in particular has no dependency on any other account issue (I have normal, working HubSpot access myself) — so this isn't a downstream effect of anything else on my end.

Troubleshooting already tried:
- Reauthorized each connector individually via the OAuth flow (confirmed "Connected" afterward)
- Restarted Claude Code
- Opened a brand new session in each of the three products above

This is blocking real business work (I run a medical clinic).

Environment: Windows 11, Claude Code VS Code extension, Chrome (web app + browser extension).

### What Should Happen?

I have 4 claude.ai-hosted connectors (Supabase, Vercel, HubSpot, Canva), all showing Connected at claude.ai/customize/connectors.

None of them are actually usable, confirmed across three different Claude products:
- Claude Code (VS Code extension) — /mcp shows all 4 as "Needs Auth"
- claude.ai website (new chat) — same result
- Claude browser extension — same result

This rules out a session-caching issue. HubSpot in particular has no dependency on any other account issue (I have normal, working HubSpot access myself) — so this isn't a downstream effect of anything else on my end.

Troubleshooting already tried:
- Reauthorized each connector individually via the OAuth flow (confirmed "Connected" afterward)
- Restarted Claude Code
- Opened a brand new session in each of the three products above

This is blocking real business work (I run a medical clinic).

Environment: Windows 11, Claude Code VS Code extension, Chrome (web app + browser extension).

### Error Messages/Logs

```shell

```

### Steps to Reproduce

1. Authorize a claude.ai-hosted connector (e.g. Supabase) via claude.ai/customize/connectors
2. Confirm it shows "Connected" with a green checkmark on that page
3. In Claude Code (VS Code extension), run /mcp
4. Observe the same connector shows "Needs Auth" instead of connected
5. Repeat in a brand new Claude Code session, the claude.ai website, and the Claude browser extension — same result in all three

### Claude Model

None

### Is this a regression?

Yes, this worked in a previous version

### Last Working Version

_No response_

### Claude Code Version

v2.1.268

### Platform

Anthropic API

### Operating System

Windows

### Terminal/Shell

Windows Terminal

### Additional Information

_No response_

No source files or tests are identified. Start by reproducing the authorization flow and checking the connector state with /mcp across Claude Code, the claude.ai website, and the browser extension; done means the connectors remain usable instead of showing "Needs Auth" after authorization.

Written by the indexing model from the issue text.