docs: apply C1 rebrand to connector.mdx

[mindymo]

Updates docs/connector.mdx with the C1 rebrand:

• Renames ConductorOne → C1 in prose, comments, and placeholder text
• Updates brand color #65DE23 → #c937ae
• Lowercases GitHub org name in the repository resource link

URLs that are case-sensitive or functional (distro site, tenant URLs, email addresses, file paths) are unchanged.

[github-actions]

Claude finished @mindymo's task in 39s —— View job

---

PR Review: docs: apply C1 rebrand to connector.mdx

• Gather context and read changed files
• Review changes against origin/main
• Post review feedback

---

Looks good! This is a clean, consistent rebrand across the doc file. All 22 substitutions are straightforward and correct.

What was checked:

• All prose references ConductorOne → C1 — consistent and complete
• Brand color #65DE23 → #c937ae — updated in all 7 icon instances
• GitHub org name lowercased in the repo link (github.com/conductorone/baton-retool) — GitHub URLs are case-insensitive, so this works fine
• Functional URLs left unchanged (container image ghcr.io/conductorone/baton-retool:latest, etc.) — correct
• YAML comments and placeholder text updated appropriately (# C1 credentials, <C1 client ID>, etc.)
• No orphaned references to the old brand name remain in the file

No issues found. Approving this change.

[gontzess]

LGTM - single file rebrand change