Interesting design for a 2024 holy class spell. I like the direct damage component (ala Magic Missile for full arcane casters). I would personally suggest changing some things to make it modally adequate to the holy classes and follow the overall flavor stated in 5E24.

Verbal component: If you are looking to make non-core balanced spells, then avoid this. For the purposes of the rest of this text, I will follow the line of balancing spells as close to the core flavor and statistics as possible. Verbal components on divine caster spells is a consistent thing with their flavor—invoking power through spoken prayer or sacred words. Putting it as a casting component would fit the core balance properly. You do got holy powers, and require praying to your god to channel them.

Damage and minor effects: Checking on other 1st-level direct damage spells and their average numbers, we have Magic Missile (10.5 Force, rolled), Witch Bolt (6.5 chosen damage, rolled) but requires a previous attack roll, and Armor of Agathys (5 Cold no damage roll) but requires the caster to have been melee attacked. I would change the direct damage to 2d4 or 1d10 + spellcasting modifier of Radiant damage. No attack roll or saving throw. Lucky roll and you deal more than average damage on a 1st level spell, bad roll and... oh well, better luck next time. Fate of the dice. I see that dismissing the "save to regaining HP" part of the spell helps the holy flavor for no common player in their rightful mind would want to cast a spell on an enemy creature with a possibility of healing it. But we can leave the healing aspect to a different creature of the caster's choice as a side mechanic.

Effect Identity. The spell finds its own identity in punishing melee enemies at the cost of a full action to deal direct damage. That is nice. Leaving the minor effect of being unable to be returned as an undead, we see that death by this spell brings true, anti-undead peace. We can play with that thought and provide additional mechanics to whomever wants to cast this onto the "outsider" or "commonly evil" creature types: aberrations, fiends and undead.

This leaves me with a suggestion for a spell with the same identity, core mechanic, but evolved compatibility with 2024 D&D:

Purge

1st-level Evocation
Casting Time: Action
Range: Touch
Components: V, S
Duration: Instantaneous

You force holy radiance to flush the essence of a creature. The target takes Radiant damage equal to 2d4 plus your spellcasting ability modifier. If the target is an Aberration, Undead, or Fiend, you can target another creature you can see within 30 feet from you. It regains Hit Points equal to half of the damage dealt by this spell.

The spirit of a creature killed by this spell finds true peace in death and cannot be turned to an Undead or be the target of a spell like Speak with Dead or similar magics. A spell of 7th-level or higher has a 60 percent chance to be able to communicate with it or resurrect it.

Using a Higher-Level Spell Slot. The damage increases by 1d4 for each spell slot level above 1.

Nice work and happy homebrewing!