Let's say I have 10 Firestore databases in different projects. Out of these 10, 8 have small Firestore database size which falls in free quota. The other two are larger in size and exceeds the free quota.
Now my question is, does Google charge on a per project basis, or does it charge for the resource across all projects of the same account?
A single project can at the moment only have a single Firestore database. See How to create multi environment DB's with Firestore
But if it were possible to have multiple databases (such as with the Realtime Database), the free quota is per project, not per database within that project. So the total operations on all database instances in the project are added together, and then you get billed for the total.