Spanish vainilla is a diminutive of vaina, a sheath or pod, from Latin vāgīna. The later English word vanilla arrived through New Latin.
New Latin mediation is omitted from the cards because its form matches English. Earlier English vaynilla was borrowed directly from Spanish and replaced; it is a separate earlier borrowing, not a step before New Latin.
Source
Merriam-Webster: vanillaNoun Word History gives the Latin base, Spanish diminutive, New Latin mediation and separate earlier English borrowing.