What to think when asked to self-fund research?
Answering for the UK and for not-STEM: YMMV in other locations or subjects.

In such a situation it is very likely that you have not been given the funded position. If I were to speculate here, the internal decision about the funded position was likely made and whoever contacted you assumed you had already been notified that you did not get it. However, it is certainly acceptable and appropriate for you to ask about the status of that application and you need not hesitate.

However, to put things in perspective, my subject area recently had over 100 applicants for 4 funded PhD positions (and 86 applicants for a single post doc position). It certainly didn't matter at all who applied first as no one looks at the applications until the closing date, and we don't look at them in the order they come in. While you might believe your application was strong, and it might be strong, if you are facing a similar applicant to award ratio, your prospects aren't good.