And I'm not a legal expert and I'm not from the EU, but it sounds like obesity is considered a disability under EU law, at least in the workplace, according to an article from 2014. The change was due to a 2010 case from Denmark, actually, so you've probably heard about that.
And if it's something that can impair professional life, obviously it will impair personal life. So, I would question the decision that you aren't disabled. If you can't fit into the shower, that's clearly a disability. I would request a new caseworker, or whatever they'd be called in Denmark. And maybe it will take time and maybe you'll still have to make due in that new apartment, but keep pushing.The court’s advocate general over the summer in an opinion on the case said obesity could be described as a disability if it “has reached such a degree that it plainly hinders participation in professional life”.
Edit: Just saw your edit. Yes, that is also the case here. People fall through the cracks all the time and there are far too many cracks that are far too large. Lots of kids go hungry here, too and disabled people end up on the streets all the time. The poor and disabled are worth nothing here either and are treated like scum and scam artists. And many of them are ignorant of the systems that can either help or harm them. But you aren't in that position. You still have a home. With internet. You can still work at this.
And, ok, so your church consists of humble people. But a dollar here and there adds up to a $15 cheapo microwave pretty quickly. You can also start a GoFundMe, the social safety net of modern times.