Custom MCP Server - OAuth failure

### Short summary

No login flow when adding Custom MCP server

### Affected version or release

v1.1.10

### Installation context

_No response_

### What happened?

MCP Server -> Adding a new custom MCP server.
Mode: HTTP
URL: https://mcp.app.wiz.io/
Headers: none
OAuth Client ID (Optional): none.

No auth page loaded, on the connector page or in a new chat.

Using the .github/mcp.json for GHCP CLI
`{
"mcpServers": {
"wiz-mcp-server": {
"tools": [
"*"
],
"type": "http",
"url": "https://mcp.app.wiz.io/"
}
}
}`

paired with `/mcp auth` worked as expected

### Steps to reproduce

_No response_

### Expected behavior

_No response_

### Additional context

_No response_

Start with the custom MCP server configuration in .github/mcp.json and compare its HTTP OAuth behavior with the working `/mcp auth` flow. Reproduce the setup for https://mcp.app.wiz.io/ without headers or a client ID, then trace whether an auth page appears on the connector page or in a new chat; done means the login flow loads as expected.

Written by the indexing model from the issue text.