A319 First Officer reported receiving an altitude alert from ATC while on approach.

Narrative

While on the arrival; we were cleared for the ILS XXR approach outside the IAF. Cleared to cross the IAF at 3000 MSL which was lower than charted. We were in open decent down to 3;000 MSL. ATC had changed the approach segment so the PM went heads down to build the approach. The approach had 2 segments at 3000 then dropped to 2200 before the FAF. The captain (PM) asked if I wanted 2200 set. I agreed and he set 2200 for the bottom altitude. I failed to then select decent as I was still in open decent. As we approached the IAF at 3000 MSL; ATC told us to slow to slowest practical. We dropped gear and flaps and managed the speed and started the checklist. ATC then issued an altitude alert check for an altitude of 2;500 MLS. We immediately selected 3000 and pulled for open climb. The aircraft climbed back to 3000 quickly and we continued the approach without issue. This error occurred in part due to the pilot flying switching to an alternate decent mode and both the PF and the PM passed the correct altitude in descent. It should be noted that ATC issued multiple changes; laterally; vertically and speed throughout the arrival and approach phase which increased workload and vulnerability; arguably unnecessary.