fix(search): harden live search accuracy, provider queries, and request cost #32828

Job	Run time
Test and Build / Lint and Test	2m 58s
Test and Build / Test (shard 3)	2m 10s
Test and Build / Test (shard 2)	2m 22s
Test and Build / Build App	3m 39s
Test and Build / PostgreSQL integration (push)	5m 44s
Test and Build / PostgreSQL integration (migrate)	5m 4s
Build ARM64 (GHCR Only)	0s
Prepare Trigger.dev	0s
Build AMD64	0s
Migrate Dev DB	0s
Detect Version	0s
Build Dev ECR	0s
Create Desktop Prerelease	0s
Check Desktop Signing Secrets	0s
Desktop Prerelease Build	0s
Publish Desktop Prerelease	0s
Prune Desktop Prereleases	-1s
Detect Desktop Changes	-6s
Check Docs Changes	-8s
Migrate DB	0s
Promote Images	0s
Create GHCR Manifests	0s
Promote Trigger.dev	0s
Process Docs	0s
Resolve Attestation Subjects	0s
Attest Images	-1s
Create GitHub Release	-1s
Desktop Release	-1s
	21m 39s

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