How to do per-tenant backups for multi-tenant databases?
Postgres has no feature to ferret out semantically a subset of the rows in your tables. Nor does any other database I’ve heard of. 

You will need to write your own code to retrieve just the one tenant’s rows from each of the relevant tables. This code might be in your app, or might be done on the server within Postgres. 

Also, you’ll need to decide if any other tables not split by tenant should also be copied into each tenant’s backup.   

I have heard about some database vendors considering features to support multi-tenancy explicitly. The database would understand that the data for each tenant should be considered separate and kept in logical and/or physical silos. But I don’t know of any such products  ready for production yet.