In principle you could ride every type of mountain bike in the Mullerthal. But the best upgrade would be a dropper-post, unless you are completely comfortable going downhill with your saddle up.
Tyres should have good grip and must not be worn out.
E-bikes are welcome but be aware that the extra weight also needs to be lifted upstairs or over fallen trees. See it as free and extra core stability training.
Last but not least make sure that you bike is technically in good condition. We are cycling through large woods and the nearest bicycle store is a long walk and....... probably closed.