Stories where the main character is a librarian

[Lobstergirl, au gratin]

No Offense

[Rainbowheart]

Weather
Out of Body
In the Stacks
The Librarian
The Little Clan
The Giver of Stars
Wonderland Creek
Strange the Dreamer
The Pages of the Mind
The Camel Bookmobile
A Lush and Seething Hell
The Girl He Used to Know
The Bookshop on the Corner
The Awakening of Miss Prim
The Library of the Unwritten
The Accidental Beauty Queen
The Library of Unrequited Love
Mayumi and the Sea of Happiness
Home for Erring and Outcast Girls
The Book Woman of Troublesome Creek
The Sexy Librarian's Big Book of Erotica

[Sheila]

The Mobile Library mystery series by Ian Sansom

[Ingo]

First book of that for the click:
The Case of the Missing Books

[Robin]

I've scrolled through the suggestions but didn't see the Magical Cats series mentioned. Fun cozy mysteries with a touch of paranormal.

[Jessica]

Key of Knowledge, The Ice Queen and Strange the Dreamer fall under the speculative fiction category.

He's male, but the protagonist in The Time Traveler's Wife is a librarian.

The rest of these, not really speculative, but perhaps something would interest you:

American Wife
Open Season
Smoke in Mirrors
The Librarian of Boone's Hollow
Beyond All Dreams
Here Lies the Librarian
Secrets of the Blue Hill Library series (Guideposts)
Dylan

[Lobstergirl, au gratin]

Stones from the River by Ursula Hegi

[Rachel]

Jaye wrote: "Librarians in Fiction: A Critical Bibliography
"The depictions of librarians in over 374 nov..."

This sounds amazing, thank you!

[Lobstergirl, au gratin]

Meiselman: The Lean Years

"The dark comedy Meiselman details the workplace maneuverings of an aggrieved librarian as he attempts to finally gain recognition by hosting a controversial author for a book talk."

[Maria]

The Empty Crown by Rosemary Edghill.

Main character is a librarian as are her friends and coworkers in the first and second book (this is an omnibus of 3 books. The series didn't continue after the 3rd). I haven't read the 3rd yet. Not sure if it's relevant but she talks about how and why they're in library school, working for the library. It's Urban Fantasy.

[Rainbowheart]

Bad Animals
The Paris Library
The War Librarian
The Littlest Library
How Can I Help You
The Blackout Book Club
Miss Morgan's Book Brigade
The Lonely Hearts Book Club
The Librarian of Burned Books
The Library of Borrowed Hearts
What You Are Looking For Is in the Library
The Department of Rare Books and Special Collections

[Gillian]

Midnight at the Bright Ideas Bookstore by Matthew J. Sullivan takes place at a bookstore rather than a library, but otherwise meets most of your criteria.

[Darcey]

Turning Pages

[Lobstergirl, au gratin]

Look at Me