Also, in general, if you have legal residence long-term in a country, most countries do permit a route to obtain citizenship. Norway does appear to do this too (though it’s not a guaranteed right, and you need to learn Norwegian as part of that process). Thing is, I don’t know whether legal residence in Svalbard – which is a Norwegian territory, but not part of Norway proper – counts as legal residence in Norway for naturalization purposes, and I could very much believe that that is not the case.

https://en.wikipedia.org/wiki/Norwegian_nationality_law

Foreigners may become Norwegian nationals by application after residing in the country for at least seven of the previous ten years, while holding a work or residence permit valid for at least one year. Applicants must be at least 12 years old, demonstrate proficiency in the Norwegian or Sami language (or alternatively complete 300 hours of Norwegian language courses), intend to reside in Norway permanently, pass a good character requirement, and not have a criminal record.[11]

Thinking of an analog, I know that in the US, American Samoa is unusual in that while it is a US territory, American Samoa wanted to run their own immigration policy (because there are people in (non-American) Samoa who they wanted to be able to move in). Both the US and American Samoa were willing for American Samoa to be a US territory, but the US wasn’t willing to have American Samoa just be a back door to general entry to the US if they had different immigration policy. Normally, in an American territory – like Puerto Rico, say – the residents are American citizens. However, because of this independent immigration policy that American Samoa runs, based on the arrangement that the US and American Samoa worked out, American Samoans are not actually American citizens – they are American nationals. While generally they can live and work in the rest of the US, just the fact that American Samoa is okay with someone moving to American Samoa and has the right to let people in as they choose doesn’t necessarily mean that the same person can use that status to just bounce from there to legal status in the rest of the US.

It wouldn’t surprise me if Norway has similar restrictions on people bouncing via legal residence in Svalbard to broader Norway, because the situations are somewhat-similar.

EDIT: Yup.

https://www.lifeinnorway.net/living-on-svalbard/

It’s also important to understand that time spent living in Svalbard does not count towards residence in Norway. That means that if you’ve lived in Svalbard for two years, those two years will not count towards a permanent residence application in Norway.