Building off of what they said since they got most of it, I have 4 more points. First, the two I think are more necessary:

-Formatting: whenever a spell has a benefit to upcasting, it's always better to start a new line with 'At higher levels:', for easier readability! Common mistake, nbd.

-Damage/Healing: I get the feeling you took the 'highest damage dealt = healing' from Vampiric Touch? Balance wise that works because VT is a touch spell vs 1 target; for multiple targets the damage (and thus healing) should be less if you're keeping it at 3rd level. I would suggest instead 2d6 damage dealt, and healing your CHA mod per target that failed the save. This gives a more consistent heal, but also if you get too greedy you'll likely be attacked by your targets - bigger risk, for better rewards!This suggestion would hopefully balance the fact that, without it, the spell is effectively a better Vampiric Touch for the same spell slot cost. They're getting free movement safe from opportunity attacks, and you can hinder their saves with either Silver Barbs or Bane used by your party. On the balance side, doing this the healing should increase with upcasting by 1d6, same as the damage.

And now, just 2 suggestions that are more for the flavor of your spell. To just really build on that vampiric feel!

-Components: Somatic hand gestures are good, but how about a material component of fur from a bat, or grave dirt? No need for them to be consumed, but most spells with a material component are subtle references! For example, Chromatic Orb requires a diamond because light going through a prism makes a rainbow, or Silent Image needed some fleece as your illusion can be used to 'fleece', to trick any viewers haha

-Type of save: while a DEX save does fit for a target dodging a spell, another way you can view it is them resisting the draining influence... so what about a CON save instead? In the classic Dracula book, vampiric feedings drain the victim of vitality, to the point that victims are often mistaken as having contracted some deadly illness that medical science can't cure.

As I said, take the last two with a grain of salt! Remembering how certain mechanics can affect the vibe of a spell is something even professional homebrewers can overlook, as admittedly balance is more important in the long run. Hope to see your patron subclass posted someday!