feat: add sidebar integration connect shortcut

[Zeko369]

Summary

• add an accessible plus button beside the sidebar integration list
• open the existing integration picker from any console route without changing the current route
• close the mobile navigation drawer before showing the picker
• cover the sidebar entry point in the recorded provider-catalog scenario and add a patch changeset

Problem

Connecting an integration required returning to the integrations page and using its page-level Connect action. The persistent integration list in the sidebar had no equivalent shortcut, which added friction when users noticed they needed another integration while working elsewhere in the console.

The picker state was owned by the integrations page, so the shared shell could render the integration list but could not open that existing flow.

Fix

The existing connect dialog is now reusable by the shared shell. The sidebar section header includes a compact, labelled plus button that opens that dialog and records the same analytics event as the page-level action. Desktop keeps the current route visible behind the dialog; mobile first dismisses the navigation drawer so the dialog has the full viewport.

Verification

• bun run lint
• bun run format:check
• bun run --cwd packages/react typecheck
• bun run --cwd packages/react test (335 tests)
• cd e2e && bun run typecheck
• recorded self-host run of scenarios/provider-plugins-ui.test.ts
• rendered desktop and 390 x 844 mobile interaction checks with no console warnings or errors

Screenshot