So I know it takes your bonus action instead of your action and can't make people prone, but does the limit on size class for a normal shove also apply to the shove with Telekinetic?
The size limitations only apply when shoving with the Attack action.
In the rules for melee attacks, we see:
Using the Attack action, you can make a special melee attack to shove a creature, either to knock it prone or push it away from you. If you're able to make multiple attacks with the Attack action, this attack replaces one of them.
The target must be no more than one size larger than you and must be within your reach. Instead of making an attack roll, you make a Strength (Athletics) check contested by the target's Strength (Athletics) or Dexterity (Acrobatics) check (the target chooses the ability to use). You succeed automatically if the target is incapacitated. If you succeed, you either knock the target prone or push it 5 feet away from you.
These rules apply when you use the Attack action to make a special melee attack to shove a creature.
The Telekinetic feat does not use these rules at all; it uses its own rules as described in the feat description:
As a bonus action, you can try to telekinetically shove one creature you can see within 30 feet of you. When you do so, the target must succeed on a Strength saving throw (DC 8 + your proficiency bonus + the ability modifier of the score increased by this feat) or be moved 5 feet toward you or away from you. A creature can willingly fail this save.
Since there is no mention of size, there are no limitations concerning the size of the target or the one doing the shoving.