I'm a Venezuelan immigrant in Spain. I'm not in an illegal situation, I'm already a resident, however, somehow I feel a bit like you. I mean, I'm a civil engineer, but I can't work as a civil engineer in Spain until I pass through a long paperwork process. Europe needs (or the major institutions always say they need) professionals from abroad. However, they don't make it easy to bring them here, to Europe.
Europe is famous for red tape and bureaucracy. In fact, even though it is no longer a super power in the traditional sense like the USA, people describe it as a bureaucratic superpower, since it's the planets best source of unnecessary rules that can actually influence the rest of the world (such as forcing Apple to use USBC). So I feel you!
One major problem causing the collapse of the UK is that it's also obsessed with red tape, but it's actually quite useless and unqualified to do it XD depended on the euro too much, so when Brexit happened, they realised they had no idea what they were doing... Sigh