Custom connector fails with "Couldn't register with sign-in service" even though OAuth is disabled server-side and no request ever reaches the server

### What happened?

Setup: Self-hosted MCP server (ha-mcp / Home Assistant Webhook Proxy add-on) exposed via a Tailscale Funnel URL that shares its hostname with the Home Assistant frontend (https://.ts.net/api/webhook/mcp_).

Error shown when adding/reconnecting the connector in Claude.ai:
"Couldn't register with HA's sign-in service. You can try again or add an OAuth Client ID in the connector settings."
Reference IDs: ofid_ed49191c92da3a35, ofid_ee07732d977a3018

What I verified before reporting:
- OAuth is confirmed disabled on the MCP server itself (Webhook Proxy add-on "Enable OAuth (Beta)" toggle is off, OAuth Mode unset).
- The server is publicly reachable (confirmed via mobile browser on cellular data, landing page loads correctly).
- The webhook add-on has a "Log inbound requests" debug option. With it enabled, retrying the connector's "Connect" produced zero inbound request log lines — meaning the connector never even hits the webhook endpoint before failing.
- Earlier the same day, before this error started appearing, the identical URL worked fine (multiple successful 200 OK POST requests logged from Anthropic's IP range 160.79.x.x).

Suspicion: the connector's OAuth auto-discovery may be picking up Home Assistant's own built-in login/auth endpoints (present on the same origin/hostname) and attempting Dynamic Client Registration against those, rather than treating the webhook resource as unauthenticated — without ever calling the webhook path itself.

Happy to provide further logs if useful.

### What did you expect to happen?

MCP connection to Home assistance green over Claude (was working the day before, no config changes in between)

### Steps to reproduce

Claude connector HA will not connect (connection not possible)

### Area

MCP Connector (adding/managing servers)

### MCP Server (if applicable)

_No response_

### Error messages or logs

```shell
cant find any incomming connection in the logs - using my mobile phone from external and point to the MCP url will work and generate logs.
```

### Additional context

_No response_

Start by tracing the MCP Connector's OAuth auto-discovery and Dynamic Client Registration flow for a webhook URL sharing an origin with Home Assistant's authentication endpoints; verify whether registration is attempted before the webhook path receives a request. Done means an OAuth-disabled connector reaches the configured MCP webhook and connects without requiring an OAuth Client ID, with coverage for this same-origin case.

Scritto dal modello di indicizzazione a partire dal testo della issue.