Learn Croatian: Švicarska je vrlo bogata država. - Switzerland is a very rich country.

Švicarska originally comes from the adjective for "Swiss" (implicitly modifying a dropped noun like zemlja or država). Because of this, it declines using adjective endings rather than standard noun endings. While its nominative form here ends in -a like a regular feminine noun, its locative form is u Švicarskoj (in Switzerland), which uses the feminine locative adjective ending.

If Švicarska historically means "the Swiss country", isn't adding država at the end of the sentence redundant?

It might seem repetitive literally, but it is perfectly normal. Adjectival country names like Švicarska or Hrvatska are treated entirely as proper nouns in modern Croatian vocabulary. Native speakers don't actively process them as descriptive adjectives anymore, so explicitly calling it a rich država (country/state) sounds completely natural.

Would the sentence still be grammatically correct if we dropped the word država?

Yes, absolutely. Švicarska je vrlo bogata is a complete and natural sentence meaning "Switzerland is very rich." In that version, bogata simply acts as a predicate adjective describing the subject, rather than modifying a trailing noun.

Why doesn't the word vrlo change its ending to match the feminine noun država?