Postgres soft delete partition, what to do with Foreign keys?
A table of 1.3M rows is pretty small.  It would be unusual for a table of that size to benefit from partitioning.

Have you looked at the queries which are slow with EXPLAIN (ANALYZE, BUFFERS) to see what the problems are?

When partitioning works well, it is because it works hand-in-glove with your use cases.  So there can't really be generic partitioning advice.  You would have to tell us much more about the types of queries you run and what your performance expectations of them are, and what the current execution plans look like.