Unfortunately due to the huge amount of waste produced by guinea pigs, they don't lend themselves well to naturalistic or bioactive housing.
Eco earth is too dusty to be used dry, and used moist would cause URI and foot issues. Plants could be used, true bamboos, grasses, herbs, safe wild plants and weeds, however these will be very quickly eaten and needing replaced on a near daily basis and may end up over doing their quota of fresh food.
I'm not sure about cherry branches but cork rounds can be used as tunnels for them, however they'll quickly become soiled if not frequently cleaned which can cause ammonia build ups and again, respiratory issues.
I know of people who keep exotic/wild species of cavy and even they do not use completely natural set ups, we just cannot provide the kind of space for these animals to make it work with how much waste they produce, even for their smaller exotic cousins.
The most natural we can provide is a deep layer of woodshavings (at least 5cm) and a good, deep layer of hay (I do at least 30cm) to allow for burrow creation, tunnels, hides etc can be wooden, which appear more natural, you can, as said, offer them areas of grass in the cage however this won't last long at all