[RPG] Can a Way of the Open Hand monk’s Open Hand Technique prevent Legendary Action reactions

Yes, the monk can knock creatures of any size prone.

Other methods of proning specify their size limitations, for example, under Shoving a Creature:

The target of your shove must be no more than one size larger than you, and it must be within your reach.

And similarly, under the Battle Master's Trip Attack:

You add the superiority die to the attack's damage roll, and if the target is Large or smaller, it must make a Strength saving throw. On a failed save, you knock the target prone.

The Monk's Open Hand technique just says:

Whenever you hit a creature with one of the attacks granted by your Flurry of Blows, you can impose one of the following effects on the target:

• It must succeed on a Dexterity saving throw or be knocked prone.

Since it doesn't include any limitations or restrictions, there are none.

The next section is a textwall: The tl;dr is that prone just isn't that powerful.

As far as this being unbalanced is concerned, I think you're overestimating the impact of the prone condition. The effects of the prone condition are to make attacks from adjacent squares more accurate, and attacks from a distance less accurate, as well as making the prone creature's attacks less accurate.

None of this is a particularly big deal, and since any creature can end the prone condition just by spending half their movement, it's unlikely they'll ever feel the penalty imposed on their attacks. In effect, the prone condition merely increases the accuracy of attacks from adjacent squares until the creature's turn, then costs them half their movement.

Furthermore, for this feature to work, it requires a successful attack followed by a Dexterity saving throw. The target creature effectively gets 2 chances to defend against this effect. It's also worth considering that some monsters (for example, elementals) are immune to the prone condition, so this simply won't work on them at all.

Finally, remember that ki points are the Monk's main resource, and they are quite scarce, especially at low levels. Spending ki points is meant to have a significant impact, otherwise they wouldn't be quite so rare. If the effects you got from them weren't useful, the Monk class would just be a weaker version of the Fighter.

away

is the critical word here. In plain language, the direction of motion should be along the line connecting the monk and her target, which is typically going to be horizontal (or near-enough as to not matter).

If you want to take a squat before striking and hope that "pushing away" now lifts the creature, we've got rules for that: lifting (PHB 176). But now we're squarely into rulings territory: a GM might reasonably rule that you must successfully grapple before lifting, as you're trying to impose movement. A GM might reasonably rule that you're making a shove attack, and that shoving someone 5' horizontally is physically akin to shoving them 6" upward (citation: every fight I had with my brothers as a kid). &c. &c. &c.