Yes, it's a powerful feat... but is it overpowered?
I don't know, to be honest. But let's compare it to other feats.
For example, the description of the Chef feat states (TCoE, p. 79):
- As part of a short rest, you can cook special food, provided you have
ingredients and cook's utensils on hand. You can prepare enough of
this food for a number of creatures equal to 4 + your proficiency
bonus. At the end of the short rest, any creature who eats the food
and spends one or more Hit Dice to regain hit points regains an extra
1d8 hit points.
- With one hour of work or when you finish a long rest, you can cook a
number of treats equal to your proficiency bonus. These special
treats last 8 hours after being made. A creature can use a bonus
action to eat one of those treats to gain temporary hit points equal
to your proficiency bonus.
That's basically a small potion of healing, and you can use it once per short rest... and once per day, you can give temporary HP... and that's all for free.
Or the description of the Magic Initiate feat (PHB, p. 168):
Choose a class: bard, cleric, druid, sorcerer, warlock, or wizard. You
learn two cantrips of your choice from that class's spell list.
In addition, choose one 1st-level spell from that same list. You learn
that spell and can cast it at its lowest level. Once you cast it, you
must finish a long rest before you can cast it again using this feat.
Your spellcasting ability for these spells depends on the class you
chose: Charisma for bard, sorcerer, or warlock; Wisdom for cleric or
druid; or Intelligence for wizard.
Choose the cleric list for the feat; spare the dying and cure wounds and do basically the same without a healer's kit.
There are good feats, there are not-so-good feats, and there are feats that are so situational that you don't ever use them.
So, is Healer OP? I'd tend to say no - but it is one of the better feats.
A thing from the comments
Darth Pseudonym commented:
I'm not sure one cure wounds per day comes anywhere close to basically
giving everyone a free hit die of healing per short rest.
Well, yes, an additional HitDie for everyone pretty much sounds like a Mass Cure Wounds, but it isn't the same. Take the following situation as an example:
You go into combat full life with 50HP. You get knocked down to 2HP and have to fall back. Now only a Cure Wounds, False Life or a spell with similar effects can save your day, because any additional hit can push you into dying state. Additional HitDice during short rest doesn't do anything for you in that situation, because there are only 50HP + potential temporary HP available for you. Every in-combat healing you receive pushes that number up... but additional HitDice during short rest don't.
Hence in-combat healing is much more valuable than off-combat healing. Use it wisely and accordingly to the particular situation you're in. Is it a question of life and death and you don't have time for off-combat healing? Use a spell. You have the time for a quick in-between-combat-chowder? Eat the chowder. ;)