You may be overthinking this.
First it says on p. 195 of the PHB:
Contests in Combat
Battle often involves pitting your prowess against that of
your foe. Such a challenge is represented by a contest. This
section includes the most common contests that require an
action in combat: grappling and shoving a creature. The DM
can use these contests as models for improvising others.
However, I don't think it is needed to invoke this; the Shoving a Creature attack says:
If you win
the contest, you either knock the target prone or push
it 5 feet away from you.
Where the creature starts is irrelevant - it ends "5 feet away from you"; in front, behind, left, right, even up or down if you like.
Edit re definition of push
A comment has been made that "push" necessitates that all force must be away from you i.e. that it is solely the antonym of "pull". Several definitions of push that I have examined do not support this. If you Google "push definition", the first that comes up is:
exert force on (someone or something) in order to move them away from oneself
This only requires that you exert force to move them away from you, pushing directly away would qualify but so would swinging them around or even pulling them initially towards you in order to push them away. Just because we have "go to" words like pull or throw to describe these does not mean that they do not also fall into the wider definition of push.
Synonyms of push include shove · thrust · propel · impel · send · press · drive · plunge · stick · force · shoot · ram · bump · knock · strike · hit · jolt · butt · prod · poke · nudge · elbow · shoulder · bulldoze · sweep · jostle · bundle · hustle · hurry · rush · manhandle
Pull is an antonym, however, there are multitude of ways of pushing someone so they end up on the opposite side of you without having to pull them.