Any bureaucratic hurdles when partly moving abroad?

Hi all, I have worked and lived in Vienna for the last 3 years, and have my Hauptwohnsitz here. I will start a new job in September in another EU country, but I will keep my flat here for another 3-4 months. I won’t have any income in Austria anymore in those months.

I was wondering if there is anything special I should take into consideration in terms of taxes, bureaucratic hurdles or other official rules regarding partly moving abroad?

Apologies for writing in English, but my administrative German is not that strong 😬 Many thanks in advance for your advice!