If you have more than one Google Cloud project and only connected one initially, you don't need to redo the whole GCP integration setup for the rest.
Go to Setup → Integrations, find Google Cloud Platform, and click Manage:
Add more discovered projects expands to list any additional GCP projects visible to your already-connected service account — pick from that list rather than reconnecting from scratch. Since this looks up projects live from GCP, it'll fail if the connection can't currently reach your GCP account (an expired credential, revoked access, etc.) — in that case, fix the connection under Update first.
This is separate from Add New Integration, which connects an entirely different GCP account or service account rather than adding a project under the one you already have connected.