What are the complete sets of tools an HVAC engineer or technician should have?

An engineer and a technician are two completely different career fields requiring different educations and who do different tasks. 

Most engineers will use very few hand tools in their careers. But they would need ink pens pencils calculators and perhaps a flash light if they go into the field to instruct a technician on how to solve a complex warranty task.So your list is meaningless, sorry. You are also at least dozens of tools short on your list for a technician. sockets, ratchets, flash lights, pocket or torpedo levels, vacuum guages, vacuum pumps, manometers, volt ohm meters, extension cords, drills, drill bits, caulk guns... the list just goes on and on and on.  Even simple items like a broom and dust pan to clean after you are finished have to be carried in your truck.

reported, not asking a question

Elhigh is spot on in his answer and in his comment toward Steven. Steven is an idiot. The only one who believes Steven isn’t an idiot is Steven. His mother also knows he’s an idiot. 

As far as drivers, a standard 10 in 1 is usually good enough. Anything else you can use wrenches for or a small socket set. If you’re doing commercial, make sure you have an Allen for lieberts, a triangle key for Stulz and a small punch or screw driver to pull the pin on Data Aire switches.

Steven F, I dislike you because you’re an ignorant, arrogant ********. I would gladly put my knowledge and skills against yours any day. You are an idiot. If you want, I can tell you that to your face.  

For a change I'm somewhat agreeing with Steven F, although where he gets off declaring you are the least qualified person to answer is, typically for him, absolutist, uninformed, and unfair.  Chill out, Steve.  Just because you CAN be mean to people and get away with it doesn't mean you have to.

Speaking as an HVAC pro with decades of experience, I cannot help but notice you didn't mention ANY HVAC-specific tools: 

No gauges

No leak detection equipment - though the garden sprayer with soapy water can be surprisingly effective

Let me ask: why "hammers various?"  I've never needed a hammer in any work I've done.  What are you beating on?

No torches?  None?  And you're making joints how?

No reco equipment mentioned at all: vac pump, sucker, reco tank.

Digital multimeter

Pipe wrenches?  Uhh, maybe, if you're working on towers.  For res work pipe wrenches are a bit on the overkill side.

This IS NOT a question, and YOU are the least qualified to answer.

In fact, no one that believes there CAN BE a single correct answer is qualified to answer.

ehigh is again projecting HIS faults on me because he doesn't like me. The reason HE insists of proving is I am RIGHT more often than he is, precisely because I DON'T think I know everything. His answer actually EXPLICITLY agrees with everything I claims I am wrong about.

redstapler dislikes me because he KNOWS I am right more often than he is. He also contradicted himself in his claim he agrees with ehigh.

there are various consumables that you'll also need -- among them; mastic, fungus killer, electrical tape, spare sheet metal screws in multiple sizes and lengths, insulation board [you'll be making plenums], HVAC tape [aluminized], solder, aluminum cover for new hvac lines, screws and anchors for same, masonry drill bits [and battery powered drill to use them in], expanding cell foam sealant, J clips to secure the new HVAC lines to the building, spare filters in multiple sizes, and probably another couple of dozen that I've forgotten  -- oh, yes -- and a whopping lot of patience will be needed to deal with homeowners who ignore instructions and never service their units ever [until they stop working].  Hmm -- I left out stuff related to swamp coolers [if they're used in your area]. ...

Gauges You need the correct gauges to read the pressures, tape measure, a bucket or two. rags, insulation cutter, razor knife, oscillating saw, hack saw, tube/pipe cutter, solder kit, volt meter, power drill and bits.

Here was my list in addition to yours.

PPE equipment

Coil fin straightener

Flaring & swaging Tool Kit

Tubing cutter

PVC cutter

Hack saw

Torch - propane map/oxygen

Manifold gauge set

Micron Gauge

Multi meter

Sling Psychrometer

Shrader valve tool

Tin snips sheers set

Allen Wrench Set metric / standard

Channel locks

Caulk gun

Fuse puller

Infrared thermometer 

Temperature Humidity Meter (Fluke 971) 

Airflow Meter/Micromanometer (Fluke 922)

Noncontact voltage tester

Tape measure

Flashlight(s)Small and large cordless drill …. bits and driver fittings

HVAC Load Calculator

Nitrogen Regulator

Torch set

Soldering set

Vacuum pump

Recovery Machine

Reciprocating saw

Sheet metal hand tools

Wet/Dry vacuum

Gage set, vacuum pump, electrical meter, gas meter, amp meter, spring benders, swaging set, torch with multiple tips, tubing cutter,