Under the current policy, are there extra points for cohabitation after postgraduate studies in Australia?

Yes, both sides can add 5 points.

This immigration points policy has been implemented for many years, and is specifically called "spouse points".

The prerequisite is that both parties are spouses. In Australian immigration policy, cohabitation is also a form of spouse, but the review is stricter and requires applicants to submit more proof of living together; then both parties apply for immigration at the same time (same case), and one of them is the main applicant. The other party is the deputy applicant; the third party is that both parties meet the basic conditions, such as passing the professional assessment, passing the IELTS score, etc.