A few words of clarification follow:
Maybe Camunda could clarify the interplay between bpmn.io and the Camunda modeler
bpmn.io provides modeling toolkits for BPMN, CMMN, DMN. They can be easily set integrated into a web-page (that is what you see at demo.bpmn.io, for instance).
I thought the Desktop version is based on bpmn.io, and the respective .js libraries.
Correct. The Camunda Modeler is a desktop application. Under the hood it builds upon Electron, an environment to build applications with web technologies. We embed our modeling toolkits in there, too.
Is it possible to use the template function anyhow at the web based Camunda modeler as well?
Quick answer: No.
Element templates is a feature that is provided as part of the bpmn-js-properties-panel. It actually has only a very small footprint inside the modeler itself.
The reason we do not do not encourage the use of element templates outside the Camunda Modeler right now is that it is not public API and may change any time without notice. Refer to the hint in the element template docs, too.
Because of that, we cannot provide any support for that stuff, too. If you still feel like you should use them at your own risk, checkout the implementation in the properties panel.
Hope this clarifies things. Your feedback on this matter is appreciated!