docs: fix CI docs model IDs and add provider outreach

[joostboon]

Summary

Follow-up to #2152 — these changes were pushed to the branch but the PR was merged before GitHub picked them up.

• Update claude-model default and example to use latest aliases instead of pinned dates
• Add missing mcp-config-path to the optional inputs table
• Add "Using a different AI provider?" section at the bottom

Test plan

• Verify Mintlify renders correctly

🤖 Generated with Claude Code

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