Where it fits
Google Cloud combines infrastructure with managed application and data services. Compute Engine supports conventional servers, while Cloud Run runs containers without requiring a team to operate a cluster. Google Kubernetes Engine offers a Kubernetes route when cluster-level controls and tooling are useful.
How pricing works
The bill follows the products used: compute, storage, requests and network traffic have different meters. Minimum instances and always-running services can change an otherwise usage-based budget. Region selection and committed-use discounts also matter.
Choosing a setup
Firebase builds a more integrated application-backend experience on Google Cloud. Google Workspace provides finished email and collaboration software. Those are useful related products, but neither is another name for a Compute Engine account.