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With such an itinerary, you have to enter the Schengen area in Frankfurt and once you are past the border check, you can easily go to the city. As far as immigration law is concerned, a Finnish residence permit is enough for that, even if this is your first trip to Finland. Depending on where you are coming from, additional Covid-related restrictions do apply but they depend on where you have been during the 10 days before travel.
It doesn't really matter whether you stay in the airport or not, you will not be treated like a passenger in transit. In fact, if you come from an βarea of variant of concernβ (currently Brazil and Uruguay), even transit to Finland would be forbidden whereas transit to a non-Schengen country would be permitted. In other words: if you can transit, you can enter and if you cannot enter, you cannot transit (within the Schengen area).