these checks are a lot less centralised than you may imagine. The passport scan mostly just pulls the static data off the passport, so they can check it matches the printed data and that it’s validly digitally signed by the issuer. There may be some lookups in national databases, and in transnational “wanted” databases, but these are mostly done by name. There’s no Europe-wide entry-exit system (yet) so there’s generally no practical problem with mismatching the document you use to enter and leave. FWIW, most countries are similar.