I was thinking about how readers would feel about reading an episodic story that instead of having a different story per book, having a different story per chapter. Not an anthology, but like same MCs, different happenings. And really what issues come with that formatting.
I am wondering what I should look out for if I decide to format it like this. It should be noted that they are web novels and the individual stories are rather short.
This is certainly something that you can do, if I understand you correctly, and it has been done before with great success.
It certainly has been quite common for authors of short stories to hit upon a popular character or a winning formula and to write more and more short stories featuring these characters: say an observant and prodigious detective or an ingenious and resourceful valet. These can then be collected into single books. I appreciate that there is a difference if you are setting out from the beginning to write a collection, but there is certainly a precedent.
Arthur Conan Doyle's Sherlock Holmes stories consist of a number of short stories (as well as a few novels) which were collected together. For example The Adventures of Sherlock Holmes contains 12 short stories featuring the detective.
Similarly P G Wodehouse's much-beloved Jeeves stories began as short stories in magazines which were collected (and sometimes rewritten) into books. Occasionally a single story (often originally written as a single story) will span 2 or 3 chapters, but often one chapter is one story. For example Very Good Jeeves contains eleven stories. After Very Good Jeeves Wodehouse mainly wrote novels.
I would say most readers of Sherlock Holmes or Jeeves alive today did not read the original stories in the original magazines but bought the collections of short stories and, well, if your efforts are half as successful as Sherlock Holmes I reckon you'll have done alright. So certainly it can work.
This sounds like the format of the 1986 science fiction novel "Tuf Voyaging", by George R. R. Martin. The protagonist is an eccentric space merchant who chances into possession of a powerful, ancient bio-warship. Tuf decides to give up merchanting and go into business as an itinerant genetic engineer, offering his services to different planets. Each chapter is a different story about Tuf's adventures with his new occupation. Most of the chapter-stories can stand alone, but three use the same secondary protagonist and setting, which gives the novel a connecting backbone. A similarly formatted novel, "And the Devil Will Drag You Under" by Jack L. Chalker, places the connecting stories as bookends, at this novel's beginning and end, which sets up the actions of the balance of the stories, then makes a conclusion. Using a similar technique could help your book feel like a cohesive narrative instead of just a short story collection. I read the book back then, and found the format enjoyable and easy to read. I cannot say how other readers might feel about your novel's format, but you could employ beta readers to help you determine that. The novel and character have quite a few fans. This formatting should be workable for your novel. "Tuf Voyaging" might be worth a read for format research, even if you're not a fan of science fiction. Also, many of the episodic and collective novels that I've read have an engaging character or characters that keep readers reading.
Depending on how separate versus how interwoven the separate stories are, what you are writing is either a collection of short stories or a fix-up. As Wikipedia explains:
A fix-up (or fixup) is a novel created from several short fiction stories that may or may not have been initially related or previously published. The stories may be edited for consistency, and sometimes new connecting material, such as a frame story or other interstitial narration, is written for the new work.
As for your question how readers will receive such a work, that is difficult to predict. Sales figures seem to indicate that anthologies don't sell as well as novels. For example, Uncommon Type, a short story collection by actor Tom Hanks (so published with a big push from his celebrity status) was the best-selling anthology in 2017 with 67,459 copies sold during that year and 235,000 copies sold until 2023. On the other hand, John Grisham's novel Camino Island sold 528,000 copies from June to September 2017 alone. A well-established writer with a large fanbase like George R. R. Martin can probably sell a lot of copies of a fix-up novel like Tuf Voyaging, but for a newcomer that episodic nature of the novel will probably put off quite a few potential readers (and many agents and publishers).
It has been speculated that readers dislike anthologies because they are not as immersive as novels. Many readers (and viewers) love stories to be long because they like to spend as much time as possible with beloved characters in a beloved world. That is one reason why series are so popular both in print and in tv. Anthologies (and fix-ups) require more effort from the reader: For every story or episode they have to emotionally let go of the previous one and attempt to care for another goal (and sometimes other characters). Readers report that they don't like having to make this switch. And coming from one story or episode you like to one you like less can feel anticlimactic and make for a much more disappointing reading experience than reading a mediocre novel in the first place.
So I would assume that much of the success of your collection or fix-up depends on how well-integrated the separate episodes are, how easy the transition is from one to the other, and whether you can maintain the same level of story quality and reader satisfaction throughout.
What you have here is a short story cycle.
The collection of those into a book is called, as Ben observed, a fix-up. (Even if they are not published separately and then fixed up into a novel. The term is general.)
If they are completely episodic, it may be advisable to be sure to blurb it and all the rest as the adventures of the characters.
I love this question. You might read, if you have not already, 'Olive Kitteridge' by Elizabeth Strout for structural inspiration. Each chapter is a short story and by the end you have a strong feel for numerous, interrelated characters as you move along an arc for a few of them specifically. The installments stand alone well but en masse are very strong.
