Add Codex MCP setup docs

[thebiglabasky]

What changed

• Adds Codex to the Checkly MCP supported-client compatibility table.
• Adds an auth-method column so pre-registered OAuth client ID setups are explicit.
• Adds a direct Codex MCP setup section with the Checkly MCP endpoint, OAuth client ID, OAuth resource/audience, fixed callback port, codex mcp add, ~/.codex/config.toml, and codex mcp login instructions.
• Clarifies that Codex appends a server-specific callback path and that Checkly does not support Dynamic Client Registration.

Why

Codex is supported through a pre-registered public OAuth client for direct Codex MCP setup, not through Dynamic Client Registration or ChatGPT connector setup.

Validation

• codex mcp add --help
• codex mcp login --help
• Parsed the documented TOML snippet with Python tomllib.
• git diff --check
• npm exec --package=mint@4.2.259 -- mint broken-links

npm exec -- mint validate was also attempted. It reached build validation but failed on the existing /snippets/copy-prompt-button.jsx warning about importing react, unrelated to this change.

[mintlify]

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Project	Status	Preview	Updated (UTC)
checkly-422f444a	🟢 Ready	View Preview	Jun 24, 2026, 1:09 PM

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