They are very similar actually, but permaculture is about more than just agriculture, agriculture is one of the sides of permaculture. For me syntropic agriculture is that side, some people also call it agroforestry but this term is used for other kinds of agriculture, which builds forests but differently. On syntropic the main difference is very high density of plants and extensively pruning. The video I posted in the first comment you see a few people doing research on automating this processes, there's also some people Swiss investing into this, sure with less biodiverse but its being working great for them, so yes, can be automated, also lots of machines used on fruits crops can be used on this system, specially to speed up pruning bigger trees. And usually on syntropic its not common to find "key" shapes beds and stuff that we see from permaculture, its usually straight rows, which helps a lot with automation I guess.
Introducing an idea, in case you haven't encountered it elsewhere already. There are some estate-farms in England that are arriving on the same conclusion of permaculture/syntropic ag, albeit from a different angle.
They were spending a lot of money to extract marginal agricultural products from soil that wasn't well suited to monoculture, and some eccentric estate managers decided to stop spending the money, and allow the estates to "re-wild": no more shrub pruning, earth-moving, etc.
One of the "big ideas" they had, which might be useful to you, is to reintroduce "mega-fauna" to their ecosystems (in their case, ponies, "wild-ish" bovines, pigs, goats, and deer. They found that these fauna did an excellent job of pruning the wilds, but they had a new, second-order problem in pruning the fauna; they'd like to reintroduce wolves, to do the culling for them, but can't for somewhat obvious NIMBY reasons. :)
They're at the point where the estates more or less run themselves; they mostly make income from selling flowers, culled remains, and ecotourism.
Anyways, all this to say that you might consider leveraging some organic automatons to do some of the "extensive pruning" for you. Herds of goats in particular are very efficient pruners, and they can pay for themselves.
