Going with your subject typo, a "beastmaster" could have a suite of weapon-equips that are its collected beasts; they equip in different slots. A weapon slot one could be "leech", which replaces all existing status effects with just bleed. With more fantastic creatures in the game, you could have a "healing monster" that gets equipped there for direct HP healing. Could be gory and be a "Trophy Hunter" class that has Unicorn Horn for healing, "Lamprey Jaw" for what I described as leech and so on.

Don't forget about non-standard weapon types we see in certain games: "books" and "scrolls" as weapons (also bells, cards, dice, rackets, whips, cloth sashes, dolls, calculation tools...). For a physical object, it could be an aspergillum or censor, either of which could have base weapon and off-hand equip for "what goes inside it" [what liquid or what incense].

If you're doing "punch to heal", any weapon type works, though usually blunt more than piercing. (Rapier of Healing doesn't have quite the ring to it.)

Swords that steal life energy from the target and transfer it to their wielder, there were items like this in Baldur's Gate 2:
https://baldursgate.fandom.com/wiki/Adjatha_the_Drinker
https://baldursgate.fandom.com/wiki/Sword_of_Chaos

And if you're asking "Why does it have to be swords", I say, just because.

As far as weapons that can physically assist with healing, rather than just having healing spells attached to it, I think the dagger is most appropriate.

You can make incisions for help in removing bullets and arrows.
When heated, it can cauterise wounds.
You can cut out necrotic tissue.

Probably not the best tool for amputating limbs though. Bonesaws are traditional, but may not be very good as a weapon. An axe perhaps?

If we bring magic into it, something that had would be well suited to saving life - the 'principle' of sympathetic magic in action.
Ignoring talking swords and stone golem extracts, wood seems the best. So clubs and quarterstaffs.

A quaterstaff also fits in nicely with the rod of asclepius, the symbol of medicine.

The normal Ûbercharger is the best, as this clip clearly proves:

https://www.youtube.com/watch?v=l62OY19rZ7k#t=687 (at 11:28)

Or Makai Kingdom's syringes. (Basic attack heals, while all techniquest are HP drain attacks that don't work on buildings. All attacks are RES based.)

I think you may have misunderstood the concept of a weapon. ;)

The Bazooka launcher that shoots healing syringes... Can't go wrong with that...

ive seen all kind of items/abilities with healing , probably even bazooka too
I dont get what is the best for healing , when you can give healing to anything

The second expansion for the original Neverwinter Nights RPG, Hordes of the Underdark, has an intelligent sword that steals health and gives it to the wielder … [slight spoiler, look away now if you haven't played the game and might do so…] initially. (You can find Enserric in Chapter One.)

He also cheerfully announces the type of monster you are fighting, which is handy if you aren't sure (there are all sorts of magic items and class bonuses that give benefits against classes of monsters, like Outsiders or Undead, and some of these categories may not be immediately obvious.)

I was sure it would be a hammer, but for some strange reason, all my patients die

the question is pointless without context. A mace? A dagger? A staff? A gun? Hyperdemic injector? a lantern? bare handed? an axe? a wand?

Why not a syringe? (Makai Kingdom has syringe as a weapon type; the basic attack heals, while the skills steal HP. The attacks don't work on buildings, however.)

Yes, as i said, without context it is a pointless question, it can be everything and nothing. And thank you for proving this point by needing to add context to your syringe weapon.

Of course, thinking of "beast" type (yes, there's a typo in the topic title, which unfortunately can't be edited by normal users), I note that Fell Seal: Arbiter's Mark, with the DLC installed, has a way to get beasts to heal with physical attacks; combine with the ability to make the normal attack an area attack, and the fact that the attack only heals allies (enemies take damage as normal), and you now have a really good healer that uses physical attacks to heal. (Just make sure to do this with a high attack monster.)

now, now.... keep in mind that "(Again, this is outside of the context of a specific game.)"