If any plant and planet pairing in this material has a genuine ancient pedigree rather than a Renaissance one, it is the oak and Jupiter.
The oracle at Dodona in Epirus was sacred to Zeus and was read in the sound of a great oak, the rustling of its leaves, and in some accounts the sound of bronze vessels hung in its branches. Homer refers to it in the Odyssey, Herodotus gives an account of its foundation, and it is among the oldest oracular sites in the Greek world, with archaeological evidence of cult activity well before the classical period. The oak is Zeus's tree in Greek cult before anyone drew up a table of planetary rulerships, and Jupiter is Zeus.
The pattern repeats outside Greece without needing to be borrowed. The oak is Thor's tree in Germanic religion, Donar's Oak, felled by Boniface at Geismar in the eighth century as a demonstration that the god would not defend it, and Perkunas's in Baltic religion, and Perun's in Slavic. All of these are thunder gods, and all of them are attached to the oak.
There is a plain physical reason for the convergence, and it is worth stating because it explains the whole cluster. Oaks are struck by lightning disproportionately often: they are tall, often stand isolated in open ground, and their deep-fissured, water-holding bark conducts a strike destructively rather than flashing over. A tree that is visibly and repeatedly hit by lightning attracts a thunder god. Culpeper later repeats the Jupiter attribution, but here he is reporting something far older than himself.