#7761 improvement(search): simplify integration setup and connection actions

Summary

• Show one member row per integration, reuse authorized accounts across sources, and keep new-account actions inside account dropdowns.
• Consolidate sync actions with confirmation and cooldowns; preserve source permissions when removing connections.
• Align setup controls with chip components, simplify Slack and GitLab forms, restore selector arrows, and refresh Search guides and screenshots.

Type of Change

• Bug fix
• Documentation
• Other: UI improvements

Testing

• Full application suite: 49,914 passed and 185 skipped with four workers. Shared components: 222 passed. Focused setup/action regression tests: 156 passed.
• App and component TypeScript, lint, all 46 repository audits, and docs manifest checks passed. All 10 Search guides compile and their 25 image references resolve.
• Reviewed current setup and action states with live local UI and component fixtures; recaptured changed styling. External provider authorization and indexing were not repeated for every provider in this pass.
• The default fully parallel local run hit one timeout in an unchanged metadata-resolution test. Its 52-test file and the complete application suite passed with lower worker concurrency, without changing timeouts or assertions. All CI test shards, build, lint, and database checks passed. No local production build.

Checklist

• Code follows project style guidelines
• Self-reviewed my changes
• Tests added/updated and passing
• No new warnings introduced
• I confirm that I have read and agree to the terms outlined in the Contributor License Agreement (CLA)