Deprecate and fix `search` #6336

Job	Run time
E2E tests (shard 2/2)	2m 32s
Check graphql-codegen has been run	2m 47s
E2E tests (shard 1/2)	2m 34s
Lint	1m 45s
Type-diff	2m 8s
Unit tests with Node 26.1.0 in windows-latest (shard 1/2)	2m 21s
Type check	1m 33s
Unit tests with Node 26.1.0 in macos-latest	2m 34s
Knip (unused code check)	40s
Unit tests with Node 22.12.0 in windows-latest (shard 1/2)	2m 25s
Unit tests with Node 26.1.0 in ubuntu-latest	2m 31s
Unit tests with Node 26.1.0 in windows-latest (shard 2/2)	2m 30s
Breaking change detection	1m 32s
Unit tests with Node 24.1.0 in windows-latest (shard 2/2)	2m 21s
Unit tests with Node 24.1.0 in ubuntu-latest	2m 32s
Unit tests with Node 22.12.0 in ubuntu-latest	2m 32s
Unit tests with Node 22.12.0 in windows-latest (shard 2/2)	2m 21s
Unit tests with Node 24.1.0 in macos-latest	2m 34s
Unit tests with Node 24.1.0 in windows-latest (shard 1/2)	2m 21s
Unit tests with Node 22.12.0 in macos-latest	2m 35s
Bundle	1m 29s
Check OCLIF manifests & readme & docs	1m 39s
Unit tests	2s
	48m 18s

Provide feedback