US Citizen here. Applied for Temporary Residence Permit in Hungary via the Private Entrepreneur pass. I've stayed in Schengen for over 90/180 days now. Most of it is in Hungary. Hungary and the US have an agreement that allows US Citizens a 2d 90 day stay visa free. So my overstay in Hungary is NOT a problem. I stayed about in Poland and Italy a total of 21 days this last 180 days.
However, when I get approved for the Temp Residence Permit, does it restart my 90/180 clock in the rest of the Schengen countries? Or does my stay in Hungary NOT count towards the 90 day period?