Resource overlap between Synapse databases

I have an Azure Synapse dedicated pool with a single database. It is scaled to DW500c which the documentation says means it has a single compute node.

If I add a second database how does work against it affect the first DB’s resources? Will the second DB reside on the same node as the first, or will the second have its own dedicated memory & compute?

Having tried it and queried sys.pdw_nodes_pdw_physical_databases from each DB I see different values for pdw_node_id between the results. This makes me think they are separate hardware (VMs, k8s containers, whatever) but I cannot find documentation to confirm or deny my hunch.