That way, AFAIK, the German government will determine that the "place of effective management" is Germany, and tax you also there.
Double taxation is not better.
I would say that depends of the company's legal form. If you have an "AG" or "GmbH" you get double taxed anyway, one time the company and than again your salary. So if you have an Estonian equevilant of a GmbH/AG your company will get taxed by Estonia and your salary by Germany. The Estonian E-Residency Website at least confirms my assumption but in case of Germany I could be very well wrong of course...
https://www.e-resident.gov.ee/understanding-cross-border-tax...
Have multiple friends who have done an Estonian OÜ despite being primarily German. No issues on this tax side.
DE & EE should have a double taxation agreement.
https://www.fin.ee/en/double-taxation-agreements