Dashboard lights started flickering and triggering all the warning lights?

Hello, was the Aux battery replaced? And which wire going to the engine was he checking that had only 6 volts on it, going to the fuse box in the engine compartment? The smell of burning plastic can either be the insulation on wires or if wires are touching/ or laying on a surface that gets hot like the exhaust manifolds or pipes. Both batteries in the vehicle need to be in good condition, both should be load tested when fully charged. But we would need to know what wire(s) he found that were burnt, there should be heavier gauge red wires which run from the batteries to the fuse box in the engine compartment.
Also look for any discolored connectors or fuses, if a fuse has a loose connection, it will overheat and become discolored, it doesn't need to be a blown fuse to be an issue. If it has high resistance, it can still cause all kinds of problems.

Okay, did he repair any of the harness that was burnt, or did he leave off somewhere? Wires can overheat due to high resistance somewhere in the circuit, any shorts to ground should have blown fuses, if he was left with the 6volt issue that's something where I would start to do voltage drop testing from battery positive and work my way to where the 6v reading came from, testing with a meter on DC volts should show the problem area. From B+ to almost any fuse in the engine compartment fuse panel should show close to 0volts because there shouldn't be any voltage lost.

Anything can have a parasitic drain on it, and it can be a tough test to do if not familiar, each door latch, hood, trunk, etc, need to be latched and locked, then the vehicle's network needs to go to sleep, each make has different module timeouts. But test leads and a meter need to be prepared ahead of time, so nothing wakes up during testing. Checking for voltage drop across fuses in the millivolt range can also indicate a draw on a fuse, any voltage drop on a fuse means there is current flowing through that fuse.

They replaced the lumbar actuator with a new one and it still didn't work, and they let the vehicle go like that? Its possible, but with burnt wires I would be more concerned with fire hazards, The wiring diagrams show the driver's seat with adjustments is powered by a circuit breaker, so as soon as the current flow is low enough, such as when turning the key off, the circuit breaker is going to close again and power will be restored to those circuits. I do see a connector for the lumbar section of the seat, connector 1334A if you want to disconnect it, or unplug the entire seat switch and see if your battery draw disappears.
Here are the wiring diagrams for the driver seat, the 2nd is the OEM diagram.

This is a guide on battery draws, there is method of checking for low voltage drop across fuses (in the millivolt range (mv). This is a better method than pulling fuses, just having a meter set on DC volts, low setting and looking for any very low reading can indicate current flowing through that fuse, this requires the vehicle being prepared first though.

https://www.2carpros.com/articles/car-battery-dead-overnight

With the voltage at 14.5v, that's a pretty normal level for a newer vehicle, charging system voltages are higher now. But I would suspect there still may be an underlying issue, especially since there was a burnt wire as well. There might be a wire somewhere that's intermittently making contact with either the exhaust pipe or the body. Some shorts to ground are not always apparent, I have seen many that are not fully short to ground all the time, where the insulation on a wire is partially exposed and not making contact all the time. So, when you say the voltage is lower every time you start the vehicle, do you mean you're noticing a lower charging system voltage directly at the battery, or are you checking it at the B+ stud on the alternator?
I would see if there were a difference in voltage at the battery vs the alternator output stud, if there's a difference in voltage levels, there could be an issue with the wiring between the two. I would also check the voltage level from battery negative to the engine block and frame/body. Thats a voltage drop test on the ground side, it should read very close to 0-volts.

I would put a multimeter on it and check it at the battery + and alternator + post, to be sure it charging correctly, that looks a bit strange to me, granted these more modern charging system will vary the voltage depending on different conditions, but I don't like the way it's changing like that. It looks like when you're coming to a stop the alternator is raising the voltage level, possibly if the battery current sensor or ECM is seeing a low voltage condition somewhere, when it's not actually the case, I will go over service info on this and get back to you, can you provide the vin # so we can check this specific vehicle.

That fluctuation amount is okay, the voltage does seem to be a little bit high, I would think if you have most the electrical loads off, (ie A/C, rear defrost, blower motor, etc.) It should come down if just cruising at light throttle, to maybe around 13.7v range. Here is some service info on the charging system and operations. I would check it with a multimeter to make sure the voltmeter on the cluster is correct. I don't see any warning lights on the cluster in the video, it may have been that the ECM needed to relearn some strategies since I'm sure the mechanic had the battery disconnected at some points, which might explain the higher fluctuations you were seeing previously.
Check the battery voltage before starting the vehicle and see what the static resting voltage is at, then check it at idle and 2,500 RPMs with a multimeter on the battery. That way you can be sure the cluster reading is correct. If he replaced the entire fuse block, there may have been high resistance internally, I have seen the solder cracked and broken inside a fuse box that would make contact when it was hot then as it cooled off the solder joint would open back up causing issues.

These AC voltage outlets are controlled by their own AC Inverter modules, does this still have to do with the flickering dash lights? The charging system voltage fluctuations are normal. Is that a home circuit outlet tester?

This is a wiring diagram of the AC voltage inverter in your vehicle, along with the operations. You can see the Body Control Module sends out an enable signal as well as monitors the AC voltage inverter module, so I would have the Body Control module scanned for any trouble codes, before assuming there is a fault with the inverter, The BCM will set trouble codes if it sees something wrong with the inverter. Since the AC inverter is powered by a DC voltage feed, a home outlet tester may not read or measure the same as it would a home outlet, where there is a positive, neutral and ground wire, whereas with the inverter in the vehicle is not putting out any AC voltage on the module's ground wire. Vehicles are designed to run on a DC voltage, and in fact, sometimes when an Alternator fails (such as a diode fails internally) the Alternator will start to put out AC voltage spikes which can actually damage modules in the vehicle that are designed to only run on DC voltage, in this case a 12volt DC feed.
If the AC outlet in the vehicle is not working when you plug in something that runs on AC voltage, then the module needs to be diagnosed, its power (fuse) and ground would need to be checked. But again you would almost always see a code stored in the BCM due to a fault. Are you still having the issue with the Instrument Cluster flickering?