Regarding the comments that these Disney videos are often wrong, in this case, the video is corroborated by the creators’ own words that the setting of the 1989 film is mostly based on the Mediterranean and Italy (note they falsely assumed the 1837 story was set near Denmark even though there’s no indication of that):
"Howard pitched us the idea of a— one of the very first things when we talked to him, he said, ‘Are you thinking this movie is going to be strictly set in Denmark? Because I have this idea that I want the music, because of the seaside motif of you know, mermaids and water, that this way of contemporizing the music by having it have calypso and reggae elements in it.’ We very quickly said we’re totally open to that idea. We think of this as a fairy tale world that’s not strictly set in Denmark in the 1700s."
-John Musker, (0:20 in the video, though I don’t know which interview the clip is from) https://twitter.com/lazyariel/status/1557920419805642754?s=46&t=8ndOf4ksDgx8xckHR8GGqQ
There’s also this passage from the book, The Disney Princess: A Celebration of Art and Creativity, which quotes John Musker’s words from the DVD commentary of the 1989 film:
“The Disney artists moved the story from the frigid Baltic of Andersen's native Denmark to a warmer, sunnier that suggested the Mediterranean, probably off the coast of southern Italy. Elements in the costumes and building suggest an equally vague time in the late seventeenth or eighteenth century. Musker says, ‘Rowland Wilson- he's a great draftsman-designed the Prince's palace. He did a drawing that we loved that combined these Mediterranean elements, making it a palace unlike any other Disney fairy tale palace, with the whitewashed stucco. He was really going for a warm southern Mediterranean feel that he thought would be attractive to a mermaid who'd been stuck all her in life in the cold ocean.’”
The art director of the 1989 film, Michael Peraza, Jr, had also stated on his blog and in interviews that the design is inspired by the Mediterranean and Italy:
“Eric's castle was a Mediterranean theme”
michaelperaza.blogspot.com/2010/03/the-making-of-mermaid.html?m=1
“We tried to do something kinda Mediterranean and a little bit of an Italian flip put into it also”
-Michael Peraza, Jr (14:35 in the video) https://youtu.be/6s8pHjo_EOo
I also noticed in earlier comments that some people are arguing that Eric’s kingdom can be Denmark despite having palm trees because Denmark also has palm trees at Palmestranden beach. If you look at photos of the beach, it only has short palm trees (which are generally hardier in cold weather), not the tall palm trees that are seen in the 1989 film (and mentioned in the 1837 story). Also, if you go to their website, it states the palm trees are moved into a greenhouse during the winter, indicating that they wouldn’t survive Danish winters on their own. The beach is likely a fairly recent creation that didn’t exist during the period the 1989 film takes place in
https://www.toppenafdanmark.dk/en/frederikshavn/what-do/palmestranden-palm-beach
Lastly, there’s the fact that Eric’s kingdom grows grapes in the 1989 film (the 1837 story also mentions vine-covered hills, likely referring to vineyards). Denmark stopped growing grapes following the end of the Medieval Warm Period (950-1250) and the onset of the Little Ice Age (1300-1850). The Danish wine industry has only made a comeback in recent decades thanks to climate change and newer, hardier breeds of grapes. It was even illegal for Danes to make wine commercially until the European Union approved Denmark as a commercial wine region in 2000.
https://pure.au.dk/ws/files/9153/wp_09-21