How does one export the list of stored WMS-servers in QGis?

To share the WMS connections list you can "Save" the XML file (from the form "add WMS/WMTS layer) and "Load" it in every client.

If you are on Windows, you can export the WMS settings from the registry.

For Windows XP and Windows 7, they are stored under

HKEY_CURRENT_USER\Software\QGIS\QGIS2\Qgis\connections-wms

You can export the key as .reg file, which is human readable, and import it on other computers with the same OS.

It isn't needed to edit the registry, at least for QGIS 3.x. All your connection preferences are stored in QGIS3.ini located in

 C:\users\<username>\AppData\Roaming\QGIS\QGIS3\profiles\default\QGIS\QGIS3.ini 

Look for the [QGIS] block right before [Processing] in QGIS3.ini. You can append already stored multiple connections from one user to the [QGIS] block of an other user.