Trane HVAC in horizontal position – why does evaporator throw condensation

You are correct that the refrigerant is not a consumable. If a system is low on refrigerant, then it has a leak. The technician should have a "sniffer" tool that can detect refrigerant leaks. If they didn't use it last time, then they were irresponsible. Also, refrigerant is expensive so that attitude of "if it gets low again then we know you have a leak" is wasteful of your time and money.

If the compressor in the condenser (the outside unit) is running and the air is not cool, then you are probably low on refrigerant. Frost on the refrigerant is also a pretty clear sign of low refrigerant.

I am additionally concerned about the condensation on your duct work. Is the air handler inside the conditioned envelope of the house? If so, that could explain the condensation you are seeing now but would not be seeing normally.

Condensate drip and accumulation are normal, especially during the summer months.

It is also very normal to find the drain lines terminated close to the house as you have described. Whether it is acceptable I guess could be argued based on the volume of water in question and where it is collecting.

If the accumulation of water is getting worrisome, you can buy some small diameter PVC pipe and reroute or extend your existing drain lines. You can even get creative, such as routing them into existing downspout drain lines, or directly burying the condensate drain lines themselves.

If you are worried about exterior-drained condensate freezing, you could bury a standard 4" drainage pipe to redirect your condensate. This pipe could accumulate your condensate via a catch basin, direct piping, or other means. The probability of an entire 4" pipe freezing, especially in the southeastern US, would be approaching zero.

Be sure to maintain a good slope when extending any lines, and drain to daylight any buried lines.

Additionally, you can drain your condensate to some acceptable locations inside your home, such as a plumbing drain (not a plumbing vent stack!).

Use this as a reference: