Do states still get to count “3/5 of all other persons”, presumably including non-citizens residents, illegal aliens, etc. in determining their congressional quotas?
No. It was superseded by Article 2 of the 14th Amendment, which states “Representatives shall be apportioned …counting the whole number of persons in each State, excluding Indians not taxed…”.
The 3/5 Compromise only applied to federal census-takings for the purpose of figuring the number of Representatives. (ETA: And direct taxation.) It was superseded by the 14th Amendment which provided that:
Your question reflects a misconception about the 3/5 clause. The distinction between full persons and 3/5 persons was between free persons and all other persons, not between citizens and all other persons.
Non-enslaved resident aliens, then and now, counted as full persons for purposes of census enumeration.