Processes in Microsoft 365 for setting up Office apps, redeeming product keys, and activating licenses.
Hello!
I managed to solve the problem myself!
Macros/VBA and the Equation Editor in Word are working correctly again.
Apparently every single Office application shows a different error message.
After another several unsuccessful undertakings I've tried the macro recorder in Powerpoint and it told me that STDOLE2.TLB couldn't be registered.

So I googled around a bit found out that this might have something to do with permission problems regarding this registry key:
HKEY_CLASSES_ROOT\TypeLib{00020430-0000-0000-C000-000000000046}\2.0
Apparently the whole key was missing here. So I exported the key on a Win7 virtual machine in order to import it again on the faulty machine.
Unfortunately it didn't work again because of permission problems.
So I changed the owner of the key 00020430-0000-0000-C000-000000000046 from TrustedInstaller to Adminstrators and gave the Users full access.
Afterwards I could successfully import the .reg file and voilá, everything worked.
I changed the owner back to TrustedInstaller (you have to input "NT Service\TrustedInstaller" without the quotes in the owner field) and set back all the permissions.
Maybe this post is useful to others with the same problem.
Here is the missing registry key for those who need to import it:
Windows Registry Editor Version 5.00
[HKEY_CLASSES_ROOT\TypeLib{00020430-0000-0000-C000-000000000046}\2.0]
@="OLE Automation"
"PrimaryInteropAssemblyName"="stdole, Version=7.0.3300.0, Culture=neutral, PublicKeyToken=b03f5f7f11d50a3a"
[HKEY_CLASSES_ROOT\TypeLib{00020430-0000-0000-C000-000000000046}\2.0\0]
[HKEY_CLASSES_ROOT\TypeLib{00020430-0000-0000-C000-000000000046}\2.0\0\win32]
@="C:\Windows\system32\stdole2.tlb"
[HKEY_CLASSES_ROOT\TypeLib{00020430-0000-0000-C000-000000000046}\2.0\FLAGS]
@="0"
[HKEY_CLASSES_ROOT\TypeLib{00020430-0000-0000-C000-000000000046}\2.0\HELPDIR]
@="C:\Windows\system32"