If you can design one skill into the game on healers, what would it be?

[LilimoLimomo]

Instant-cast ability, 20 second cooldown.
All party members within 30m of the caster have their HP reduced to 1 and gain Inviolate and Flickering.
Inviolate Effect: HP cannot be reduced below 1.
Duration: 4s
Flickering Effect: Cannot be affected by further instances of Inviolate; this effect is removed upon reaching full HP.

[Raikai]

Ability A) A way to give MP to your co-healer. Maybe transfer some of your MP to your co-healer.

That is a nice concept, but before it comes to relevance, as well as any other meaningful MP managment ideas, they need to make MP actually matter lol. Currently the only way healers can run out is by overhealing on purpose or mass rezzing, but if you need to do the latter on so many subjects (given how fight mechs are nowadays) is most likely that run is completely busted.

Make healer MP management matter and they open for MP sustain actions, from both the healers themselves, but from the non-healers as some sort of secondary group utility.

[GrimGale]

SCH: Ruin II upgrades to Kaustra

Kaustra: Spell, Instant, Recast 2.5s 800 MP 25yalms

Deals unaspected damage with a potency of 220.
Additional Effect: Unaspected damage over time
Potency: 40
Duration 12s.
Additional Effect: If the target is under the effect of Biolysis, spreads Biolysis to all targets within a 10yalm radius.

Broil:
Additional Effect: If the target is under the effect of both Biolysis and Kaustra, Broil casts against the target deal 5% more damage.

[Lyth]

Float (Ability)(Instant): Levitate into the air, allowing you to move and cast spells without interruption. Knockback and draw-in effects are twice as effective.

Warp (Ability)(Instant): Move quickly to the specified location, creating a Sigil of Return on the ground at your point of arrival. Nearby party members gain the effect 'Return'.
Additional Effect - Return: If you manually cancel this effect, you are teleported to the Sigil of Return.

I think the Tonberry's Lantern idea described in the OP is a good one. Movement support actions are really interesting.

[Katish]

{Spoiler Warning}

White Mage:
Reverse - Reverses some heal spells into damage spells. While reversed, the white mage radiates similar to afflatus misery. Could even also play into other parts of the kit.
Decoy - All party members around the object generated will transfer some damage to the object. Range could be indicated with a field of light.
(Call back to the Lost City of Amdapor [hard] boss [white mage dungeon] that can reverse healing into damage)
(Thinking the Decoy could in fact be the boss from Amdaphor but statuesque.)

Scholar:
A damage fairy that could be an alternative form to Seraph when Fairy Gauge is full (Does not consume that gauge). Converts all upgraded skills into damaging ones that consume the gauge. When the gauge runs out, the fairy reverts and heals the party.
(No need to explain especially recently. Could even be her...or invoke the method to become what she was (could be additional lore) [Statice])
New DoT or Debuff or a combination of both . ---> Artifice (single target): Consume 50 fairy gauge. The enemy under Artifice pulses dark green every few seconds for damage. Additionally: When Statice is out, the enemy that is under Artifice has its damage increased...when the enemy attacks, does damage to a percentage of the attack to itself.

Astrologian:
[Not a skill: A new card that when drawn could showcase a glaring eye from the card that then pulses outward. Buffs significantly...and adds some random element back into the cards.] (Based on the Watcher, because tech he is one of the 12 [13] and the cards are based on the 12 indirectly.) [Could be an upgraded Trait for Draw]
Spinner's Fate - Either: charms, burns, and freezes for varying durations. Randomizes on every Draw when skill is usable. Charm and freeze does not work on boss fights.
(Nymeia Skill)

Sage:
Soma (Body) - Sends out a blue aura, any ally with a shield(s) applied by you will gain Soma. Soma causes damage when those shielded allies are attacked. If that shield breaks or expires, will provide additional damage at a percent based on what the original cumulative shielded potency was.
Nous (Mind) - Applies one of your lasers to one party member, each attack they do will cause a followup attack from the laser present and provide a small barrier to that ally. Each further attack extends the barrier's potency from the initial hit. At the end of duration returns laser, barrier is removed and the remaining potency heals that ally.

[Renathras]

SCH: Ruin II upgrades to Kaustra

Kaustra: Spell, Instant, Recast 2.5s 800 MP 25yalms

Deals unaspected damage with a potency of 220.
Additional Effect: Unaspected damage over time
Potency: 40
Duration 12s.
Additional Effect: If the target is under the effect of Biolysis, spreads Biolysis to all targets within a 10yalm radius.

Broil:
Additional Effect: If the target is under the effect of both Biolysis and Kaustra, Broil casts against the target deal 5% more damage.

I proposed something VAGUELY similar to this (basically turning Ruin 2 into a combo Ruin 2 + Miasma and having Broil spread DoTs) and people generally liked the idea.

Likewise, I kind of like this one.