can anyone hint me, how I can let the Catalog Price rules be applied including tax. Means, when we set up a voucher in the system, that the discount of the voucher is taken into account incl. tax already.
You probably use Cart Rules not Catalog Rules (only Cart Rules can have coupons).
System > Configuration > Tax > Calculation Settings > Apply Customer Tax there is an option for the order tax rules which can be either
Before Discount or
Have you tried this?
Then you can set Order Totals sort order described in this doc: https://docs.magento.com/m2/ce/user_guide/sales/checkout-totals-sort-order.html