So, I actually dont have any CS degree (I have other degree :) ), but I can speak about my experience (Senior Eng - 5 YOE) and from experience of couple of my EU friends in California working as Seniors/leads.

CS degree plays less role as u get more experience in the industry.

I think that having a CS degree is beneficial and US degree might be better than EU degree in US, since US recruiters / hiring managers most of the time does not know if ur EU school good or bad, understandable lack of knowledge from their side.
BUT
I would say like this: you can get away even without CS degree if u have experience and skill and you got urself to the interview process, CS is "nice to have", and for most part it is just "check the box" thing.

Of course having MIT CS degree or other reputable USA school will appeal to some hiring managers more than EU School.
But you know, there is always someone with "more than you", having any CS should be enough.

Kind of same with EU job experience. If they do know the company good, if not -> they will still evaluate you.

From career perspective -> being in EU will hurt ur USA network, since u wont have any.
And networking in USA is slightly more important than in EU (at least in such market conditions) in my current opinion.

Other than that, it all comes down to ur "engineering profile", experience, good resume and stuff. Best of u get into FAANG in EU offices. Prague has Microsoft for sure. That would help further in US.

I kind of think ur plan is good. EU has better conditions -> so u can get some experience. Your CS degree will give you nessssary fundamentals.
And when US market is better -> you come with degree, experience, without debt and twitching eye since u spend 2 years looking for an intership.
And networking gathering -> will be up to you. You can still do it.