So sure, the wealth tax would only be on "the rich" when it first starts out but I guarantee you the middle class will be hit by it eventually.
The thing is, that money which comes from the upper levels is extremely subject to the whims of those governments; it can fluctuate wildly depending who comes into power and what their priorities are. So without some guarantees around it, I can understand the municipalities wanting a stable source of income over which they have some agency, and out of which they can reap immediate benefit from growing the local economy.
Anyway, I'd love to hear from someone in Germany how this is resolved there; but I'd assume there'd need to be some pretty structured, long-term agreements around minimum amounts, percentages of new growth, and so on.
For the taxes, it's complicated, because there are some taxes for which the cities and states can decide the amount, and others (for example VAT), from which they get a certain fraction, but the amount is decided on the federal level.
Edit: Let me add: Property taxes are very strangely regressive. You pay it whether you rent or own, and there is a minimum apartment cost, so you'll always pay, while a low income might not be taxed at all. Then, often, there is a sudden jump from apartment complex to SFH.