It’s not that weird. What they’re aiming to avoid is the situation where a developer does a bait-and-switch replacement of the original, advertised game concept to chase a new demographic with new money. If you have never experienced this, count yourself lucky. A shady developer can advertise/sell a great concept in some niche like a compelling roguelike, survival crafting game or even a cozy and artistic decorating game, and actually create a decent game with lots of potential… at first. And then when it’s collected a bunch of genuine good reviews and they realize either it’s harder than they thought to make, or it’s not making the cash flow they expected and not likely to, literally just replace the whole product, product page, everything with some generic shoot-em-up battle royale asset flip as an “upgrade” and alienate the early buyers to get a whole new audience to throw money at them until they realize the reviews are for what’s essentially a totally different game before it crashes into mostly-negative territory. You might not think something this egregious ever really happens, but it does, especially in the horrible land of Crowdfunding/Early Access.
The first example I can remember that happened to me personally was called “Star Forge” not to be confused with the more recent board game adaption of the same name. The linked post is about the internal development drama behind the scenes, but the bait-and-switch bullshit happened years ago and it went sideways very quickly and was eventually pulled from the store never to be seen again.
You could probably 3d print a square or hex shaped thing that has a slot on one end to fit onto the stopper, which will give you a better angle to grip it, work it from side to side or twist it. Wood would be another easy material option to try to make a little tool out of.
That said if it’s really stuck enough to break the handle, then you’re going to need a new one anyway, and at that point destructive measures and eventual replacement may be your only option. In this case you might try driving a long screw into it (pre-drilling a hole for the screw as necessary) or even some kind of hollow-wall anchor to give you a more secure attachment on the other side. If you have to destroy the whole thing to get it out of there, that’s an option too. As any mechanic with a blowtorch will tell you about a seized fastener, “it can’t be stuck if it’s liquid”