GoogleProvider: client_id uses OAuth app ID (aud) instead of user ID (sub)

[shigechika]

What happened?

GoogleProvider sets client_id=aud (the OAuth app ID) in AccessToken. Since aud is the same for all users of the same OAuth app, multi-user MCP servers cannot distinguish users from the token.

GitHubProvider uses the user ID (str(user_data["id"])) for client_id, which works correctly for multi-user.

Example Code

# After Google OAuth, all users get the same client_id:
token = await google_provider.verify_token(access_token)
print(token.client_id)  # "123456.apps.googleusercontent.com" (same for ALL users)
print(token.claims["sub"])  # "1098765432" (unique per user, but not in client_id)

# GitHubProvider returns user ID as client_id:
token = await github_provider.verify_token(access_token)
print(token.client_id)  # "12345678" (unique per user)

Version Information

FastMCP version: 3.2.0
MCP version: 1.26.0
Python version: 3.14.3
Platform: macOS-26.4-x86_64-i386-64bit-Mach-O