Yes they’re doing this because get this… neoliberals are right wing too. These governments aren’t nearly as left wing as republicans like to pretend. Especially in UK, the current Labor government are blairites who literally sabotaged their own campaign a few years back to take over the party.
Here’s a fact that a lot of y’all fail to get through your skulls. A tyrannical and oppressive government doesn’t necessarily need to be inherently right or left wing. However, modern day Europe is without a doubt strongly left-leaning. To say they’re right wing is straight up false, and there’s an obvious trend of modern leftist regimes being the talking heads of authoritarian policy far more so than the right.
What is considered “left” and “right” is relative to the Overton window. Also, what we consider “liberal” in America is actually social liberalism. But you’re correct that liberalism is a right wing ideology, but only if we’re going by its classical definition which is at odds with social liberalism. In America, if you’re classically liberal you’re simply referred to as “conservative.”