Your result
Spain — Exceptional Talent
Not eligible
Spain has no talent visa, and the route you have landed on is not what it sounds like — so the useful thing is to redirect you rather than encourage an application that will not succeed.
The carta de naturaleza grants citizenship, not residence, and it is granted at the government's discretion by royal decree for exceptional circumstances. In practice the grants cluster around elite athletes who are to represent Spain and people deprived of their own nationality. Being distinguished in your field, even very distinguished, is not what this route responds to — and it is not a way to move to Spain, because it is not an immigration route at all.
There is no Spanish equivalent of the UK's Global Talent visa or comparable schemes elsewhere. What Spain has instead is a set of routes that are genuinely good and considerably faster than the general system, and one of them almost certainly fits you.
If a Spanish employer wants you, the highly qualified professional authorisation runs three years, renews for two, has no labour market test and is handled by a specialist unit with short deadlines. If you are a researcher, scientist or academic, the research authorisation covers hosting agreements with universities and R&D centres, and includes twelve months afterwards to find work or start a venture. If you want to run your own venture and it is innovative, the entrepreneur route is assessed on the project rather than on capital.
Any of those gets you to Spain. After ten years of residence — or two, if you are a national of a Latin American country, Andorra, Portugal, the Philippines or Equatorial Guinea — citizenship follows on the ordinary terms.