Is there a recommended table size for partitioning in postgresql?

Question

I used RDS Aurora PostreSQL in AWS.

The size of the data I manage and the number of rows are too large (7 billion rows and 4TB), so I am considering table partitioning. (I also considered the citus of postgresql... but unfortunately it is not available in aws...)

When I request some query in that table, it is very slow... So I applied table partitioning (10 partitions) and the query performance was there, but still slow.

The site below recommends ‘Tables bigger than 2GB should be considered.’, but in this case, there are too many partitioning tables and it seems difficult to manage.

https://hevodata.com/learn/postgresql-partitions/#t10

What would be the appropriate table size?

And is the pg_partman extension required in this case?

https://docs.aws.amazon.com/AmazonRDS/latest/UserGuide/PostgreSQL_Partitions.html

Is there any other way to improve query performance other than partitioning if there is too much data in the table?