feat: fix rerenders on search input (#3784) #12667

Job	Run time
Detect Version	4s
Test and Build / Test and Build	4m 57s
Check Docs Changes	0s
Build AMD64 (./docker/app.Dockerfile, ghcr.io/simstudioai/simstudio, ECR_APP)	5m 22s
Build AMD64 (./docker/db.Dockerfile, ghcr.io/simstudioai/migrations, ECR_MIGRATIONS)	1m 41s
Build AMD64 (./docker/realtime.Dockerfile, ghcr.io/simstudioai/realtime, ECR_REALTIME)	5m 23s
Build ARM64 (GHCR Only)	-1s
Process Docs	0s
Create GHCR Manifests	0s
Create GitHub Release	0s
	17m 26s

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