Cowork: a custom MCP connector fails to connect with 502 CLIENT_HTTP_NOT_IMPLEMENTED from the MCP proxy, and only that connector, for a whole session

**Surface:** Claude Cowork on the web, cloud session, Max plan (individual), 2026-09-14.

One custom MCP connector out of ~25 fails at session start and stays unavailable for the life of the session, while every other connector on the same account connects and reconnects normally. The session reminder reports:

```
Gmail_Multi (502): "SdkHttpError dialing
https://api.anthropic.com/v2/ccr-sessions//mcp?mcp_server_id=&mcp_url=&toolbox_mcp_server_id=
(CLIENT_HTTP_NOT_IMPLEMENTED)"
```

Notes that may narrow it:

- The failure is at the **Anthropic MCP proxy hop** (`api.anthropic.com/v2/ccr-sessions/.../mcp`), not at the server: the same server is reachable and healthy from other sessions on this account.
- `CLIENT_HTTP_NOT_IMPLEMENTED` suggests a transport/method the proxy did not implement for that upstream rather than an upstream error, but nothing in the session surfaces more than this line.
- Other connectors disconnected and reconnected several times during the same session (normal churn, announced and recovered). This one never recovered across several hours.
- There is no way to retry a single connector from inside a session: `RefreshMcpTools` re-reads tool lists over existing connections and does not re-dial, so a connector that failed to connect at session start is unavailable until the user restarts the session.

**Two asks:**

1. The 502/CLIENT_HTTP_NOT_IMPLEMENTED path should be retried or surfaced with the upstream status, rather than parking one connector for the session.
2. A way to re-dial a named MCP server from inside a running session, so a transient failure at start does not cost the whole session's access to that tool set.

No repository file, test, or implementation entry point is identified in the report, so first locate the MCP proxy connection and session connector lifecycle in the codebase. Done means a failed connector can retry or be re-dialed within the running session and exposes useful upstream status instead of remaining unavailable until restart.

Written by the indexing model from the issue text.