I moved to Spain from The Netherlands as a Dutch citizen. It was a lot of paperwork, lots of planning, needed close to €10k in my bank account and needed to get private healthcare with a pretty serious health check. I had to do multiple trips to the national police office and municipalities.

That is not needed when you switch states in the US. You just need to update your address and tax records. You do not needed to show financial means and you do not need private healthcare.