Your result
Spain — Digital Nomad
Not eligible
You do not need this route, and that is unambiguously good news rather than a refusal.
Spain's international teleworking authorisation is explicitly for nationals of countries outside the EU. As an EU, EEA or Swiss citizen you already have the right to move to Spain, live there and work — remotely or otherwise — without any visa or permit. There is no application to make and no income threshold to meet.
What you do instead is register. If you are staying more than three months, you register on the Central Register of Foreign Nationals and receive a certificate with your NIE. You will also want to register on the padrón at your local town hall, which is what gives you access to a range of local services and is often asked for by banks and employers.
The things actually worth your attention are tax and social security rather than immigration. Becoming resident in Spain generally makes you taxable there on your worldwide income, and where your social security contributions should be paid depends on EU coordination rules and on how your work is structured — employed by a company in another member state, self-employed, or something in between. Those questions are more consequential for you than anything in the immigration system, and they are worth getting right before you move rather than after.
If your longer-term interest is Spanish citizenship, EU citizens naturalise on the same terms as everyone else — ten years of legal residence, or two if you are also a national of a Portuguese or Ibero-American country, which is worth checking if you hold more than one nationality.