Freelancer with Croatian Passport moving to Wien

I'm Jasenko and I'm from Bosnia&Herzegovina. My story goes like this:

I'm a contractor for the US company. Working for them almost 4 years. So basically I'm a freelancer and currently working as a contractor. I'm a graphic designer. I'm married and I plan to move to Wien.  I also have Croatian citizenship. Croatia is in EU but Austria has restrictions regarding work permits for Croatians.

I'm curious, do I need work permit to do freelance work in Austria? I can't find that information anywhere. I think I can't get the work permit because of the restriction for the Croatian citizens.

Can I get Red-white-Red card for freelancing? I plan to move with my wife and she has third country citizenship.

My logic is this: I come to Austria, I work for the US company, I don't take anyone's job spot in Austria and I pay taxes in Austria. So why would I need work permit?

Thank you!

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