While Easyjet moved aircraft onto the Austrian register, Swiss aircraft were always registered there even before the Brexit vote as they took over a Swiss carrier. The aircraft are still managed from their Luton HQ and would have been crewed anyway by locals and not UK citizens.
Wizz put aircraft on the UK register that are managed from Hungry that are crewed by Eastern European’s with many living in the UK.
Ryanair have moved Irish aircraft onto the Maltese register.
Regarding restricting Brits traveling to the EU, it won’t happen in any meaningful way if at all. Too many countries want our tourist spending money just like they want tourists from around the world.