The Verdict: Not eligible
You need no work permit: as an EU, EEA or Swiss national you can take any job in Germany freely. Register your address within two weeks of moving, and if your profession is regulated, start recognition of your qualification now.
Free movement means no visa, no salary threshold and no recognised qualification to live or work in Germany. Registration (the Anmeldung) at the local Bürgeramt produces your tax ID.
Regulated professions are the exception. Medicine, nursing, law, teaching and many trades need your qualification formally recognised before you can practise. Recognition (Anerkennung) runs through the body that regulates the profession in the relevant Land and can take months.
German citizenship takes five years of lawful residence, German at B1 and the naturalisation test, and you keep your current nationality. Free movement counts as lawful residence.