Am I missing something...or are there no "healing" traits for the "healer" Science ship?

High end Admiral traits...I mean.

Some one correct me if I'm wrong, but I believe the Techie trait improves engineering skills which will affect your repair abilities like extend shields, engineering team, and miracle worker.

Astrophysicist improves operations skills which can improve Transfer Shield Strength and Hazard Emitters.

Sci may be medics on the ground, but Eng are the 'healers' in space. Yes, Sci does have some great skills like Hazard Emitters, but Engineers can really put up the heals.

Yup. Cruisers are STO's healers/Tanks imo, while SCI ships have the hold/crowdcontrol/interups ect.

At least thats how I see it. Don't get me wrong Sci's can heal up a storm with full aux and Hzrds 3 or TSS, but a cruiser can really pump out more spot heals imo.

The heals from HE cannot compare to engineering team. Same goes for TSS v.s. Extend Shields

This. Science ships are the debuffers and mezzers, not necessarily healers. (Although they can heal)

An Engineering/Science hybrid (like the Star Cruiser or Deep Space Science Vessel) would be the best overall healer.

Note also that on the ground Engineers can set up Medical and Shield Generators, and heal shields, as well. So even on the ground healing isn't exclusive to Science either.

I am not sure what you mean. In general, ships don't get new traits as your rank increases.

Higher level ships have more and higher level Bridge Officer slots, allowing them to use more powerful skills.
As a Captain, you also acquire new powers.

Science Captain abilities that are useful for healers.

• Dampening Field
• Science Fleet

Particularly the latter is very potent, reducing the damage your team's shield takes significantly.

If you mean Bridge Officer Skills/Powers, there are no Commander level skills that heal damage. I would suggest looking into Scramble Sensors, as this disrupts the enemy team's offense and healer, and thus makes your job a little easier. (Assuming you really want to focus on healing).

The best healing science vessel is probably the Nebula, as you can mix the best science with some of the best engineering heals.

A "classic" science vessel with the regular BO configuration, I would look into a build like this:

Tactical: Tactical Team I, Attack Pattern Delta I
Engineering: Emergency Power to Shields I, Extend Shields I
Science: Scramble Sensors, Hazard Emitters III, Transfer Shield Strength III, Hazard Emitters II, Transfer Shield Strength II, Science Team I, Science Team I
If you want to be a little more defensive, then you could take EMergency Power to Shields II instead of Extend Shields I.

That is still missing a power for the Ensign slot (I would suggest going with the Deep Space Science Vessel or the Fleet Support Vessel on the KDF side)
Tactical: You will probably have to pick an offensive choice, I might go with HIgh Yield Torpedo I.
Science: You can't really use more heals, and probably also best pick something to aid your team's offense: Tractor Beam
Engineering: Emergency Power to Shields I (and now you should definitely pick up either Extend Shields or Aux2Sif1.

As I see it Cruisers and Sci share the healer-job with diffrent focuses. The Cruiser is the Hull-healer and the Sci the Shield-healer.
The combination of both make good heals, not just one of them.

My SV Healer:

DSSV - Eng Captain (But Sci would work as well)

Weapons
1 array - 1 Quantum - 1 Tricobalt on either end

25-50-25-100 power

Borg Deflector+Engine
Reman Shield

------
Consoles
3 SIF Gens
4 DefF (Induction I think)
1 Borg - 1 Torpedo
------
BOs
Tac:
TacTeam 1 - B:TSS2

Eng:
EP2S1 - ASIF1
EP2S1

Sci:
SciTeam1 - TSS2 - HE3 - CPB3
SciTeam1 - TSS2 - HE3

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Carrier is more or less identical, except BO setups and weapons (Obviously I wont be relying on torpedos with a flying whale):

Weapons 1 Array either end, rest Polaron Turrets (for their proc) - Replacable with 6beam FAW for PvE

Tac:
TacTeam1 - B:TSE2 - APDelta2

Eng:
EP2S1 - EP2S2 - ASIF2 (alt BO have ETeam3)

Sci:
SciTeam1 - TSS2 - HE3 - FBP3
TSS1 - HE2

(Tactics, Ill launch pets and start healing.. Once a few ships are beginning to shoot me (ideally Ill catch an escort about to Alpha me) I'll Delta2 and Scan3, and use my FBP - Fully Auxed, that will hurt .. alot.

The idea is to capitalize on the huge heals, even on unconsoled Hazards, while boosting TSS (and FBP I believe)