Tree one is essential. Basically, the only useful crafting comes from Soul Warden (Transformation Stones and Soulshield blue Critical sets) and Merry Potter (to support the Soul Warden).
The gathering guild mats can be purchased, and, of course, the more people have those gathering skills, the cheaper the supplies are (muds were cheap in my experience) but the Tree guild is essential.
So it’s your choice of either Muds for your Merry potter or the Trappers for your bones for Soul Shields in the end-stage.
I never really used Muds, because I leveled the crafts via pickaxes that only take Trees, and I buy the non-premium refiners, as time is money, and getting the Premium Product out faster is better imo than screwing around with non-premium.
Other option may be fishguild, because that one time I had to buy clams to craft my Charm, holy cow, I’ve regretted leveling Earthseer instead of just buying a frigging charm.
Ideally, I suggest using a mule alt at level 16 to double up on Soul Warden and Merry Potter, and if possible run both of them through the story to unlock the samples (then you can have both muds and bones, and a double Tree).
I find that two Trees + 2 MP/2SW is essential to make sure I have a cottage industry going, and there are no interruptions in the flow of pickaxes, prem primers and MTS. I am hoping that one day I will be able to open a SFTS production line.