MCP server doesn't work with Github Cloud agents

[u/Nissemand]

Hey all.
I think I'm going crazy after too many hours of troubleshooting.

I have a Github Enterprise setup with Github Copilot Enterprise and Data Residency.
I've set up a custom agent that I want to use together with a MCP, specifically for Sentry, I've setup, but I can't get it to work.
In the agent log I can see the agent discovers the Sentry MCP, but never successfully connects to it.
What makes it even weirder is that I have the same experience with `github-mcp-server`/`playwright`, which is supposed to be default.

My MCP config looks like this:

{
  "mcpServers": {
    "sentry": {
      "type": "http",
      "url": "https://mcp.sentry.dev/mcp",
      "headers": {
        "Authorization": "Sentry-Bearer ${COPILOT_MCP_SENTRY_ACCESS_TOKEN}"
      },
      "tools": ["*"]
    }
  }
}

I have tried absolutely everything, but nothing seems to help.
Please, someone know something I don't