Should I in general partition tables by tenant IDs in a multi-tenant system?
Partitioning is often more about administration (swapping partitions in and up while updating a warehouse, etc.) than performance in general OLTP scenarios and, especially if all your data is on the same drive/array, can result in a performance decrease.
If you need partitioning later you may choose to do it by a different property, perhaps partitioning such that newer, more active, data can be kept on your fastest drives. If this is the case then you have made more work for yourself as you will need to unpick the existing partitioning scheme before implementing the new one.
So while this is at least a little opinion and not 100% fact, I would say partitioning now is premature.