Although this URL is for France the advice is valid for all Schengen countries:
https://www.gov.uk/foreign-travel-advice/france/entry-requirements
Check your passport is stamped if you enter or exit the Schengen area through France as a visitor. Border guards will use passport stamps to check you’re complying with the 90-day visa-free limit for short stays in the Schengen area. If relevant entry or exit stamps are not in your passport, border guards will presume that you have overstayed your visa-free limit.
So it would seem there is no central database of entry/exit and it will rely on what is in your passport.
DJ