The prose manages to land on a fun image occasionally, but I'd describe it as quite rough to read, not seeming like it went through a lot of editing. Some lines are long and clunky to the degree that they can be difficult to parse just in terms of syntax ("Allowing myself to remember that unfortunate day wasn’t only a painful reminder of our own mortal nature but also the sole and only reference I had to the incontestable fact that he was no longer with us, and that didn’t matter much to others.")
There's also a fair amount of words being used in a slightly off manner. For instance: "the deafening silence was a stark, yet notable characteristic" – how are "stark" and "notable" in opposition? (Also, cut the whole "characteristic" part and just say it was stark.) Another example: "We organized adventures, stories, and all kinds of kids' play." It maybe doesn't sound right to say that stories were "organized"?
The central idea is intriguing, but not necessarily done justice to. I think a lot about the story feeling confusing and jarring comes down to it not using its structure well. The first moments of the game are spent on detailing the protagonist's family history, which – while not exactly irrelevant – doesn't really do much to set up the supernatural elements that come to the forefront later on. It doesn't help that the tone tends to jump around dramatically; from the solemn, tragic opening exposition, we go directly into a masturbation scene complete with some pretty silly imagery ("like Pisa, except more fleshy").
I get that the ultimate nature of the town is supposed to be a twist, but I think it's still crucial to lay out the basics of what the reader should expect early on to make the story feel like a cohesive whole. Don't want to engage in "writing a fanfic"-type criticism here, but I think there would be a lot of ways to work in some more concrete foreshadowing – what if the story opened with something cryptic involving the bear's journey, for instance?
In general, there are a lot of presentation/polish issues. Apostrophes seem to be needlessly escaped (showing up as \' in-game), some lines are long enough to overlap with the buttons, the title screen focusing exclusively on the jam is pretty weird, and maybe I suffered from some kind of technical issue, but it felt like there wasn't a lot of audio? Furthermore, while the backgrounds are nice (the illustration of the village is particularly lovely), there's a lot of stuff lingering on the screen long after narration has moved on to other matters near the beginning. It's a visual medium; if you don't have appropriate images to show, I think even just a black screen would be a preferable workaround.
It's within expectations for game jam projects to be a little unrefined and even unfinished, but I think Bear My Breath could have used more time in the oven. Moreover, it felt like it was unfortunately missing the most interesting parts of the story – the only ending you can read right now is kind of an anticlimax. If you're planning to do more with the project after the jam, I hope it can be further polished.