This looks like a very fun and promising modern take on The Little Mermaid. The early part of the first episode does take place inthe 1700's, but the final part takes us to the present.
There is clear inspiration by Disney's take (including Lara being a redhead, rather than a blonde like the book mermaid and having a secret grotto where she hides human things!), but also some (inversion of...?) the novel's religious themes?
In Hans Christian Andersen's tale, mermaids do not possess an eternal soul. They are more animal-like than human. The little mermaid wants, not only love, but a soul... Her happy ending is that she can work, doing good, for a long time, to attain a soul and enter Heaven.
A lot of modern retellings and adaptations side-step the religious aspect and just have the mer-king fear humans for whatever reason, like maybe they claimed too many of his own, or because they pollute the sea (Ponyo!), etc., so it's interesting here they see humans as cursed.
They made the witch her aunt in this version! Aaand she's ridiculously convincing. Yeah, if I was the mermaid and everybody treated my simple interest in something as inherently evil and then I got LOCKED UP IN A DUNGEON for saving a life, I might be inclined to listen too...
She wakes up in a dress rather than washing ashore, well, bare, and making it from ship sails on the beach in this version! It's fun comparing versions...
Her love was genuine, but the prince hated and feared her. She died, turning into seafoam, but was reborn... only to find her castle in ruin, her father and sisters gone, only magic mirrors that show her what she wants to see...
She gets a chance to make things right. Her family isn't dead, according to the witch, but in a deep slumber...
That "tsuzuku" ("to be continued") got me right in the heart, don't care how simple it is, the nostalgia just. WOW.