But those are luxury problems you have. The average family in BW probably also has not much more than 2k left per month after rent.
Just as an addition: I know some families with a household income of a little more than 3,000 euros per month (e.g., he’s a painter, she works part-time in retail). And after rent they come to about 2,000 euros. So it is somehow doable. They just have a different lifestyle than many here in the forum. Therefore, when dealing with such questions, one should not always base it on one’s own consumption habits but keep in mind that large parts of the population generally live more frugally (have to).
Of course, that does not mean that the OP’s project would be easy to handle. But if the OP perhaps has to move into a larger place in one or two years anyway and then no longer gets a heavily discounted apartment through the employer, he will face the same challenge as now. Only if he builds his own home, he will at least have a big advantage later in retirement because then he owns an asset in the form of a property. But if he has to rent a 5-room apartment, it will probably be difficult to build up significant wealth on the side.
Municipal plots are for many the only way to get a home, especially in areas with square meter prices north of 1,000 euros. And since such an opportunity is usually not available every day, one really has to think carefully about whether to let it pass or not (whereby the OP, probably also because of the rather discouraging comments here, has now apparently already decided). But maybe he will still find a larger rental apartment at a good price. That would of course be the more relaxed option.