Do we need to normalize user input somehow here?

no, i think is better to leave these as is, as normal string list.
nuspec doesnt show an enumeratin of values, is just like a tag about the package type.
Nuget team may have choosen to just use some tag, but instead is another property :( more complexity, few gains

also like that is less maintenance when new types are added. is really a small use case ihmo (template, clitool, dotnetool). and last two is better to be create with dotnet restore probably

Yes I'm fine with that (was basically just asking what you think)

Yes, i was thinking about it too, good question.
And to validate it too (to output the right word with the same case as nuget, to play safe).
but use case is really small