https://artificialintelligenceact.eu/
Apparently EU already works on AI regulation for more than two years and expects to continue for a year and a half at least: they project that the law will get into the full swing in the second half of 2024.
I have an impression that the major effect will be "legitimization" of AI RnD in the eyes of the public and the researchers themselves: yeah, we're not simple code monkeys, we're not just playing with (meta-)parameters to squeeze few extra percentage points of accuracy, we're doing something important, something worth regulating!
On the other hand their approach that they call "risk-based" makes sense: if you apply your system (supposedly an AI one) to something valuable like economic decision-making (give out a loan or not, hire someone or not, and so on) or driving machines that can kill people (cars, airplanes, medical devices and others) — yeah, you'd better have an independent risk assessment and mitigation certification, and other kinds of assessment and certification.