So, in the comments/reblogs/tags/whatev to this post, I have found a small yet concerning amount of people not distressed by or even outright defensive of that situation, which is why I'll explain my take on the issue in hopes of clarifying what I believe the problem is that a lot of us writers have with the approach taken above.
First of all, I mean, I have read really interesting 'inspired by' stories, like "what if"s of existent AUs, and I think that is a very similar concept that us fanfic authors in general use in relation to canon-creators, with the difference being that neither fan makes money, whereas the OG-right owners do.
Personally, I'd be honored if someone enjoyed a story of mine so much they got specifically inspired themself, and since I write for myself (I only ever publicly post for others) I might just enjoy their story in turn and everyone could be even more happy with the share of new works.
And I have also seen stories - that at some point, years after the last chapter, instead of being Continued (which has also often enough happened years after a last chap) switched from 'Hiatus' to 'Abandoned' or even explicitly 'Up for Adoption' for whatever VALID Reason - be taken over by committed fans asking the author in the best case scenario for either blanket permission or otherwise approval of their specific headcanons or originally intended direction and sometimes even be encouraged by them in return, because these authors have never stopped loving their child of love and labor they poured energy and effort into and they would in fact like to see it continued, yet are unable to do so on their own.
Now, while I personally usually only post complete works (which, yeah, didn't you know or do you simply not care that you could actually filter for that, if you were so desperate not to be left on a cliffhanger in the story???), I have to admit I do have an unfinished collab only half-way posted rn myself - for REASONS y'know like Life, Deaths, Disability, Poverty, and the whole Author's curse hitting us both - but neither of us has ever stopped loving that idea and behind the scenes we're still working on the story, and reading those comments above literally hit me right in the motivation, if not to write then to share what I've written, because I get the distinct impression that this 'continue myself' suggestion would probably mean it's getting fed to genAI ... which I do not endorse for the ressource waste, the theft and because it has no place in creative spaces in particular, but that's another topic to rant about.
And this said, all of that (inspiration for something new of their own &/ communicated adoption) is completely different to the here displayed sort of greedily impatient entitlement, of literally stealing another's work - because they're not interacting inside a community to respectfully worry about the author or politely encourage the story OR creatively putting their own spin on it as an AU e.g. like all fanfic authors do, they intend to "continue" an actual Work-in-PROGRESS, as is, to take the credit for the already existent parts themself, and spitting on the writer's bts effort and burdens.
... and all of that after 5 months, that timespan is so messing with my brain, that's not even a semester at school or Uni which could very well take up a writer's time, that's literally half the timespan of a human pregnancy, that's not even ONE (1) year as an anniversary like some milestone, that is so negligible in the grand scheme and if that story is actually as good and beloved, then it's sure as fuck well worth a wait.
If you're so motivated, write your own 'inspired by'-take on the concept. If you're so impatient, think up or write down the continuation and ending you want for yourself. But don't you dare take away another's work to publicly post for your own 'profit' and interactive attention.
That feels a little bit like a publicly offered translation, that's not declared as such, with people complimenting the translator not for the language but for the plot - which they did not work on. That feels a little bit like a publicly shared video of an imagine what if scenario, with people complimenting the poster's creativity - only that's actually just a loudly read/discussed version of your fic without credit (found lots of those on YT, e.g. in the Naruto Fandom, and I presume TikTok which I don't use).