Russians need a travel visa to go to any Western country and most of the world. Some EU countries are banned Russians from entering; the US is not issuing travel visas in Russia anymore.
EU is much closer, but it does nothing. Putins regime could've lost 30-50% of it's high-skilled workforce if EU or UK just made it easier to immigrate. E.g literally 100,000s of Russian IT workforce left due to war and political situation, but getting actual work visas is hard process and outside of country of citizenship it's only gets harder if not impossible.
But honestly west can't even help Ukraine efficiently. How can one expect EU to actually do anything to cripple Russia economy...