MCP EU OAuth flow redirects to US instance, fails with "Invalid client_id"

Bug Description

When authenticating the PostHog MCP server configured for EU (mcp-eu.posthog.com/mcp), the OAuth flow initially opens a US authentication URL. A modal then appears to
switch to the EU instance, but after redirecting, the authentication fails with:

{
"error": "invalid_request",
"error_description": "Invalid client_id parameter value."
}

Steps to reproduce:

1. Configure the PostHog MCP server with the EU endpoint:
   {
   "posthog": {
   "type": "http",
   "url": "https://mcp-eu.posthog.com/mcp"
   }
   }
2. Initiate OAuth authentication (e.g. via Claude Code /mcp → auth)
3. The OAuth flow opens a US PostHog URL instead of EU
4. A modal suggests switching to the EU instance
5. After switching, the auth fails with Invalid client_id

Expected behavior:

The OAuth flow from mcp-eu.posthog.com should directly open the EU authentication page and complete successfully without needing to switch regions.

Environment:

• PostHog account region: EU (eu.posthog.com)
• MCP endpoint: https://mcp-eu.posthog.com/mcp
• Client: Claude Code CLI (macOS)

Debug info

Start by reproducing OAuth from the https://mcp-eu.posthog.com/mcp entry point using the provided configuration and Claude Code flow. Trace why authentication opens the US URL and why the EU redirect rejects the client_id; done means the EU endpoint opens EU authentication directly and completes successfully without a region switch.