Tasha's makes official a new feat called Telekinetic which allows a caster, as a bonus action, to telekinetically shove one creature. It goes on to dictate you can move the creature 5 feet toward or away from you. So, is it a shove limited to only the 5 feet of movement or is it shove as defined in PHB where you can also opt to knock a creature prone?
The feat does what it says it does
The Telekinetic feat enables you to attempt to shove a creature, specifically to move it 5 feet closer or further away. The feat does not enable you to shove to knock the target creature prone, as opposed to shoving as a bonus action using the Shield Master feat (which does not specify whether you have to push or knock prone).
As with all things, I say talk to your DM and describe what you plan to do. Rule As Written, the feat does dictate a push or pull of 5' only, not a bonus action shove. However, as a DM I lean toward the Rule of Cool, and would allow for a contested shove to knock prone - however, I would also allow the target to use their choice of Strength or Dexterity for the save, rather than just the Strength save of the feat. Essentially, you can use a bonus action to Shove from 30' distance.
This is not true of every DM and table, so check with your DM.
Shove action is an attack option to all, not just those with the shield master feat. The only difference between telekinesis and the standard shove action is that the former is a bonus action performed with your mind and the latter is a physical action made with your body. The language in the telekinesis feat specifies that direction is irrelevant and that you can really push the opponent in any direction.
It's important to keep in mind that the telekinetic shove is invisible and coming from an unknown direction. It seems fair for a DM to rule that a PC could knock an enemy prone after a contest from an invisible telekinetic pull on an ankle, a push on the head, etc. I'd say this is DM's call.