There is no actual legal proposal at all to introduce mandatory screening (yet, anyway).

In my opinion, such legislation would be unlikely to pass EU parliament. It is more likely that the current temporary rules allowing voluntary screening get reworked into a permanent legislative proposal.

AFAIK the only relevant official procedure here is this initiative that sought feedback from affected parties (and it does not mention mandatory screening - instead it asked for opinions on what should be done): https://ec.europa.eu/info/law/better-regulation/have-your-sa...