Here’s the evidence being presented to the case:

Swift made the evermore announcement on 10 December, which is also the birthday of American poet Emily Dickinson.
Emily Dickinson ended a poem called One Sister Have I in Our House, which was one of her most romantic poems for her lover Sue Gilbert, with the word “forevermore”.
In a recent Entertainment Weekly interview, Swift talked about an idea for “this girl sleepwalking through the forest in a nightgown in 1830” (the year that Dickinson was born).
Swift’s good friend Hailee Steinfeld played Dickinson in AppleTV+’s recent series about the famed writer.
Dickinson lived in isolation for much of her life.
And just the general “cottagecore” vibe that Swift’s got going on.

Why Taylor Swift fans are convinced Emily Dickinson inspired her new album