[MCP] Linear OAuth flow fails in both CLI and Desktop App

What version of the Codex App are you using (From “About Codex” dialog)?

Codex 260210.1703, codex-cli 0.99.0

What subscription do you have?

Plus

What issue are you seeing?

I discovered a bug in the Codex Desktop App where attempting to authenticate the Linear MCP server results in no action.

In the App UI: Clicking the "Connect" or "Authenticate" button for the Linear MCP server does nothing (no browser opens, no error message).
<img width="787" height="340" alt="Image" src="https://github.com/user-attachments/assets/d73aa946-c6fc-4d00-8596-bf01748a44bd" />

In the CLI (for comparison): When I tried to reproduce this via the Codex CLI, it explicitly failed with: Error: No authorization support detected.
<img width="475" height="80" alt="Image" src="https://github.com/user-attachments/assets/15641bbd-3cf1-41d4-8325-a94cd6e3bd1e" />

What steps can reproduce the bug?

Case A: Codex CLI

Run the command to add the Linear MCP server: codex mcp add linear.
Observe the log output showing the OAuth flow starting but failing immediately with the error message.

Case B: Codex Desktop App

Navigate to the MCP settings in the Codex App.
Attempt to add or connect the Linear server via the GUI.
Click the connection button.
Result: No browser opens, and no error message is displayed in the UI.

What is the expected behavior?

For Codex CLI
When the OAuth flow starts, it should either automatically launch the default system browser or provide a clickable URI (e.g., https://linear.app...) so that the user can grant permissions. After authorization, the CLI should receive the token and confirm the connection.

For Codex App
Clicking the connection button should trigger a popup or redirect to the browser for Linear authentication. The app should then reflect the "Connected" status and list available tools (e.g., create_issue, search_issues).

Overall
The user should be able to complete the Linear integration without an "Authorization support" error, enabling the use of Linear-related tools within the Codex environment

Additional information

It appears that the OAuth callback mechanism is not properly implemented or registered within the Codex runtime for both CLI and Desktop environments. While the system detects that the server supports OAuth, it lacks the necessary "Authorization Provider" to bridge the request to a web browser.