All right this nearly 1 year long frustrating story has finally come to an end! There have been many Apple appointments, weeks of living without a computer, months of not being able to use the trackpad, Apple claiming that due to their poor design, the entire top case has to be removed, which I have to pay for even though I didn't come up with this poor design choice. And dodgy repair shops, some which refused to do something (which should be) as simple as a battery replacement, some which simply didn't know how to do it, while others claimed it's only possible with high-failure rate 3rd party batteries that will almost certainly explode. One little corner shop however, magically had access to this rare and expensive battery that Apple is otherwise not selling to anyone, and was willing to go through the risks and frustration of putting it in the machine and still give me warranty on it.
Total cost: roughly 200 USD and more than 1 week without a computer. That's less than a third of what Apple quoted! During that time I had to grade 3 videos, render multiple projects, and write a dissertation, all on an 11 year old Mac Mini. It would have been even less if I had gone straight to the second place.
The moral of the story is: if you buy a product in which the battery cannot be replaced by design, then you're pretty much asking for this to happen. In a way as consumers it's our fault that we've let this happen. Indeed we have little choice, because all laptops that have removable batteries are PCs. But there are other options, Hackintoshes, desktop Macs, or older Macs that still used to have removable batteries. Or simply, we have to know some really good repair shops and know how much time and money each repair is, and if it's worth it. If we stop paying more for products that are designed to "go bad" eventually, and start paying less for products that last longer and are built to last, then that's what we will get.
I have no idea what I will do once my MacBook Pro becomes obsolete, because a desktop seems very limiting, and I really don't like Windows, but I definitely don't want to buy a MacBook Pro again. Maybe an old MacPro that can still be repaired.