Is it correct to say that tanha is in fact an instinctive, subconscious (?), not direct controlable way of getting attached to a certain perception via gati,
while upadana is the more conscious follow up of that same attachment via related thoughts, plans, intentions, longings?
Yes. Tanha (getting attached to an arammanna) happens instantaneously. That is what is discussed in the first half of the Chacakka Sutta.
One starts thinking about that arammana only after that in the “tanha paccaya upadana” step in Paticca Samuppada.
– Once one is attached, one starts thinking about it and those are vaci sankhara. The one may do bodily actions with kaya sankhara too. That is “avijja paccaya sankhara”, which then leads to ALL the remaining steps in Paticca Samuppada. That ends up in “jati paccaya jara, marana, etc..” or the “whole mass of suffering”.
– Therefore, “tanha paccaya upadana” is really the INITIATION of the Paticca Samuppada process.