Here's some jobs that I think would work for Claire:
1) The Beepatrice Conundrum
Claire gets that job at the sex toy test lab. She doesn't get involved with the product testing but that doesn't stop Pintsize bothering her for 'free samples' or even stuff from the reject bin. This isn't the job she wants but there is a curiously high degree of skill commonality. This is especially the case with keeping the chaotic test records properly organised. As well as having Beepatrice as a common co-star, we can have Marten's reaction. Either he's always startled at Claire suddenly bringing up 'business' matters in weird contexts ("Did you know that they test these things for the ability to resist gunfire?") or he finds that he is actually a voice of experience ("Oh yeah! Mom actually has a collection of those!")
Beeps ends up calling Claire 'boss' and admits that she's relieved to have someone in the office who is 'take charge'.
2) The Crawling Chaos
Claire is literally the only applicant for a junior librarian job at Tisamonic University (an expy of Miskatonic, renamed to avoid copyright issues with the Lovecraft estate). It's a dream job - dealing with antique books, some of which are more valuable than the apartment's yearly lease value. However, the students are... weird. The running joke is that the characters are all very obviously the various Dark Gods and other eldrich abominations. They look human but their conversation often outs them. I think that this would be a lovely chance to use the parodies from Hello Cthulhu - Angry and ineffectual Cthulhu, depressive Dagon and alcoholic The Colour From Space. Oh, and Cthulhu's GF Kitty, who is a gothy catgirl domme.
Then there's the books themselves, some of which are bound in human skin, a few are written in blood, and some actually eat ink and write themselves over time. Depending on how you'd want to handle it, maybe Willow is a student there on one of the university's unique courses and has a personal relationship with a few of the more alarming tomes in general. ("Whoa! Claire! Did you know we can make peach trees whose fruits function as Death Notes?" or "Claire, The Chronicles of the Daeva say that it can give you all you want in exchange for a pint of blood. Do you think that's a good deal?")
3) Small Town Library
This the lowest energy and yet, paradoxically, the most interesting.
Claire gets a job as the head (and only) librarian for a small institution in the area around Northampton/Amhurst. It's a fairly small municipal library with a tiny budget, which is why Claire got the job. They needed someone now and they needed someone cheap. Her only co-worker is an unembodied AI who runs the catalogue and online presence. She gets a couple of weeks' training from the outgoing librarian who is old, in a hurry to leave and generally difficult to get along with because he just wants Claire to take over now so he can get on with his retirement.
Basically, the setting is just support for a lot of small-town in-jokes and stereotypes who come in and Claire has to work out what (if any) kind of book they want. More seriously, Claire's "Libraries are Srs Business" mantra is tested by working at an institution that doesn't have money and whose ultimate management chain don't care. Does she bring books home to rebind and clean up? Does she vent to Marten? Does the core cast end up helping with fund-raising (naturally Pintsize suggests a bikini car-wash and makes it clear that he wants to be part of the team).