Lets assume user_A is the owner of Dataset_A which belongs to project_A and he wants to share the Dataset_A with user_B (user_B default project is project_B).
After sharing Dataset_A with user_B (Open Dataset -> Permissions -> Add Principal -> BigQuery Data Viewer role), user_B can see project_A pinned in his BigQuery Explorer - left navbar in UI (so now he can see 2 projects project_B and newly shared project_A).
It is clear that storage costs of Dataset_A occur to project_A. But what happens when user_B queries the shared Dataset_A (i.e of user_B queries -> SELECT * FROM project_A.Dataset_A.table) ?
The query costs/processing costs occur to project_B?