On my x86_64 Slackware-Current machine in KDEs and Xfce's incorporation of system-config-printer when I navigate to "Add printer" > "Windows Printer via SAMBA" the "browse" button is greyed out.

This is/was a recurring problem throughout the years in many Linux-Distributions, in some it worked in others it did not. In CentOS 7 it did not work in the beginning, as of 7.8 (I think) it works again. Usually it was fixed by installing pysmbc for Python3.

I have compiled pysmbc from https://pypi.org/project/pysmbc/ but still no success. I managed to get it to work on on recent Linux-Distributions but not with Slackware-Current. The desired behaviour is that the browse-buttom is not greyed out. Any hint/help is welcome.

The short answer is you are trying to maintain a service based on the SMB1 protocol that is now deprecated and needs to be consigned to history.
Feel free to find another explanation with suggestions, but this hits the key points.

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Thank you allend for the link, it was very interesting to read. This sheds some light on the way Windows lists samba shares. Whether Linux does it similarly I do not know - when browsing for samba-printers on linux worked for me, it was in an environment where Windows 10 as well as Linux machines had SMBv1 disabled.

But, I have build pysmbc on another Slackware-Current laptop just now, and, lo and behold, the browse button in system-config-printer is not greyed out anymore and it does search the network. When I go to KDE's "system settings" > "printers" > "add" browsing for Windows printer via samba is still greyed out. So there is something going on with KDE's use of system-config-printer.