Our developer tried to build a sample for you: WmsAndWmts.zip (9.1 KB)
But there are some problems about that:
About your WMTS server "https://www.basemap.at/wmts/", we cannot load it maybe because security reason, please try that in your side, you can modify the code in our sample to test it.
About your WMS server, the boundingbox is incorrect from your capability:
It cannot be correct rendered under both map unit meter and decimal degree. Please modify your server side and test again.
Any question please let us know.