It's difficult to have tax residence in the place you don't live at without committing fraud, typically tax residence is linked to the place where you spend most of the year or which is the center of your personal life (e.g. where your family lives) if you move around a lot.
It's not difficult it's just not used for tax fraud/avoidance. The way it typically works in Europe is with double taxation agreements.
You can earn & get taxed in Austria and live in Czech Republic.
this works only for permanent employees, it goes out of the window if you are sole proprietor or managing director, in this case the residence matters a lot and you will be taxed additionally in country u reside in