Sonata form is a type of composition in three sections (exposition, development, and recapitulation) in which two themes or subjects are explored according to set key relationships. It forms the basis for much classical music, including the sonata, symphony, and concerto.
Ternary form is the form of a movement in which the first subject is repeated after an interposed second subject in a related key. ABA
So , this song, or any popular song, is never considered to be those forms. The, gigue, rondo and others, are considered in the classical lit.
Popular music is derived from the blues, gospel church music and a confluence of mostly African and western music. Pop music can be whatever it wants to be, with or without form, but usailly like your example, pop music will have verse 1 (or more) prechorus chorus, post chorus, verse, etc. We don't use the classical common A, B C etc but use verse chorus etc in their place. hope that helps.
you may find this interesting have a read here https://www.leonardbernstein.com/lectures/television-scripts/young-peoples-concerts/what-is-sonata-form