improvement(home): position @ mention popup at caret and fix icon con… #12909

Job	Run time
Detect Version	4s
Test and Build / Test and Build	40s
Check Docs Changes	0s
Build AMD64 (./docker/realtime.Dockerfile, ghcr.io/simstudioai/realtime, ECR_REALTIME)	2m 6s
Build AMD64 (./docker/app.Dockerfile, ghcr.io/simstudioai/simstudio, ECR_APP)	4m 4s
Build AMD64 (./docker/db.Dockerfile, ghcr.io/simstudioai/migrations, ECR_MIGRATIONS)	1m 44s
Build ARM64 (GHCR Only)	0s
Process Docs	0s
Create GHCR Manifests	0s
Create GitHub Release	0s
	8m 38s

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