After testing version 4.8.2 (versionCode 30119) I can confirm it works now.
Thanks to everyone who helped bring it to their attention. :)
If someone needs the update as quickly as possible, it's an option to use Aurora Store for that, by opening the S-pushTAN app page and selecting "Manual download" in the menu on the top right. There you'd have to insert the versionCode. It's not advised to use anything else than a throwaway Google account with that app, though, as you risk a ban of the used Google account.
As long as the App is already installed on the device, it shouldn't be a risk. After that you can delete Aurora Store again.
I don't seem to be able to upload it to apkmirror. :)