Merfolk, not mer-people
As I mentioned in my comment, the common term is Merfolk. That might help in your search for examples that fit your specific idea and flavor. A websearch for "merpeople" returned space opera and battle between worlds type of science-fantasy where the whole point is to show a clash of incompatible societies – the opposite of "just people that live their lives".
Goodreads lists 825 novels in the "merfolk genre". A brief glance at the covers and titles suggest they range from horror to paranormal romance to urban fantasy.
Based on your question, I think urban fantasy will be the closest to what you've mentioned, since it is a catch-all for fantasy and mythical tropes injected into other literary genres, recontextualized without their thematic baggage.
If I were to pitch a story idea that is regular people except everyone has elephant trunks instead of noses, it evokes a visual but has no cultural baggage (at least not in the West). It also doesn't imply what sort of plot or characters are involved, just people with elephant trunk-noses.
The narrative purpose of the 'Other'
The reason you have not seen your idea in mainstream works is because merfolk are thematically 'other' to the mundane world you want to put them in. Almost universally, merfolk are incompatible with the human world, and that's the point.
Unlike werewolves, merfolk were never human. Unlike centaurs, they don't share common goals or form alliances with humans. In medieval Europe, splicing anything with a half-woman was symbolic of menacing evil, but merfolk in particular are a metaphor for the sea itself: bounteous, dangerous, indifferent to human suffering and death. "People that live their lives" are not exotic hybrids of 2 worlds. Merfolk are not just from different environments they are different elemental beings.
Our modern idea of mermaids is not from legend, but from literature, theater, and music starting around the end of the Age of Sail, romanticizing pre-industrial life before steamships. Die Lorelei invented a mermaid interchangeable with the Greek sirens (who looked like harpies), singing to lure sailors to smash their boats on dangerous rocks in treacherous waters. The Little Mermaid and it's superior predecessor Undine account for the fairytale aesthetic – all were translated into operas and spread through the popular media in their day.
The classic trope is firm: mermaids are not 'regular' people and cannot have (christian) souls, ie: they are un-redeemable. As shapeshifting fraud-women Undine and Little Mermaid are denied happy endings despite being narratively and morally perfect.
Even 20th Century mermaid-stories (Miranda, Splash, Disney's the Little Mermaid) subvert, but confirm, their 'other' status. In comics, Prince Namor (et al) is caught between two worlds and an outsider to both. These beings are unstable by design. They represent a dichotomy, that's what makes them interesting. Sympathetic merfolk stories are often queer-coded.
Ignoring centuries of thematic purpose is… a choice. Naturally you're free to write anything you like, but it begs the question what you'd gain by swimming against the current. I don't think you will convince anyone this is a selling point, rather it goes against the tide of popular culture and would be a 'hard sell'.
You have said nothing about your story, characters, or conflict. You've suggested an idea with mixed thematic signals, but that's not a story (or a selling point) on its own. There is no inherent conflict or tension if there isn't an in-world contrast between sea people and land people. When we depict animals who are "just like humans" we anthropomorphize them by placing them in our world walking around on 2 legs. You are proposing the opposite.
Maybe it fits in the What If…? sub-genre of science fiction: What if everyone had fishtails (instead of elephant noses). Do you proceed to worldbuild realistically, adding gills, laying eggs, and leaving childcare to the males? At what point do they stop being 'merfolk' and become an alien species that evolved on some water planet? At the opposite stylized extreme, you might have a satire of modern life littered with ocean-puns and Flintstone-esque sight gags. I can't tell.
As I also said in my comment, you may find very similar stories that are not specifically fishtails, but have the tone and effect you want. Since you want to avoid traditional merfolk themes, would the My Little Pony franchise be any different?
As a writer, rather than a worldbuilder...
Ask why you want to make the fantastical ordinary. What does it say, what is the interesting angle? Does the situation 'have legs' in that it generates conflict ideas that are easy to dramatize? It sounds like you might be removing the juicy thematic elements that are appealing in the first place, instead focusing on – I don't know what... School? Lore? Royal weddings? If the intent is to re-invent merfolk without their thematic purpose, are you broadening or narrowing their appeal?
The idea is fine for an exotic setting, but it isn't exciting on its own. It's not a 'hook'. The part where you'll need to explain how it's different to reader expectations is not a selling point, but in a visual medium (graphic novel, etc) you wouldn't need to explain it at all.