How can I tell if I am short-listed for postdoc position?
I think the answer you've got was pretty clear:


If you are short listed (for interview), you will be informed.
The process (including interviews and decisions) will be completed by end of July.


Typically, the shortlist is made within a week of the application deadline and interviews are conducted within another few weeks. The decision (of whom if any to make an offer to) is typically made immediately after the last interview and then it takes some more time before an offer is accepted.

In your case, this all fits nicely within the time frame of 5 weeks (24 June until end of July). So, if above typical scenario applies, then the fact that you haven't heard from them, implies that you were not shortlisted. But there may be other reasons, such as a delay in the process.

IMHO not informing those not shortlisted at the stage when the shortlist has been made (as is the case here) is a rather poor practice.

Don't be disheartened by a failed attempt to get shortlisted at a postdoc application. There are many applicants and you must expect to make several applications before getting there. You may ask them for feedback to improve your application (but most importantly: add publications to your CV).