https://www.e-resident.gov.ee/understanding-cross-border-tax...
Estonian CIT is 0%. If you pay dividends (which is not required), or if you pay director’s salary (optional if you’re a one-man company without a ton of admin), those will be taxed in Estonia. If you only pay yourself for your actual services – no taxes in Estonia.
Germany might tax your Estonian company if they determine the company is a German resident. Check with your accountant.
(IANAL)
You might have to pay yourself a director’s salary. That would indeed be taxed at 22%, but you still only have to bill for the time you actually do admin / management work. So if you spend, say, 5 days a month on it and 15 days a month on everything else, the effective rate would work out to 5,5%.
And for a single shareholder company with no employees and under 2M € annual revenue (and probably some other criteria like not having employees or veing liable for VAT or something) it is the general practice to just not pay the director’s salary at all.
(This is probably a gross oversimplification, definitely ask a real accountant about the details.)