Every situation is different, but AC was added to the existing ductwork in my 1965 house and the existing ductwork and air returns worked okay for heating the house but were woefully inadequate for AC. I was renovating anyway but we added several returns and supplemented and upsized the ductwork for the entire house. This was a rowhouse, so essentially a townhouse. (We could still probably use a separate minisplit or through the wall unit on the top floor, but that's more of an insulation issue with our exposed rafter ceiling.

AC installations in CA require permits. Part of the permit process requires a load calculation. Request proposals from local HVAC contractors.

Your ductwork is probably undersized for cooling. A good AC contractor may be able to make some modifications. You can look at ducted heat pumps as well as the mini splits that hang on the wall.

A heat pump is environmentally preferable to a gas furnace, so maybe there are incentives for you to install mini-splits.

-Any HVAC equipment replacement or install work in California requires a permit, and it's true that permits require load calculations be submitted. Some contractors will do work without getting one. That may or not be a good idea for the homeowner to accept. Such a permit-less project would need to be disclosed at time of sale.

-OP doesn't say where the townhouse is located but a likely contributing problem could be inadequate insulation. My place in SoCal, about 20 years old and near the coast, clearly has inadequate wall and ceiling insulation. The ceiling under the attic and the interior wall on the west side get quite warm in the afternoon on sunny days. Which is to say, most days.

Insulation options should be explored. The easiest and cheapest to do something about is attic insulation and it could make a big difference for the heat upstairs. Keep in mind that attics anywhere on a sunny warm day get to well over 100 degrees so a similar temperature in the upstairs area is to be expected if insulation is inadequate, or perhaps even missing altogether.

-A split system added to the existing ductwork would probably be the least expensive option (though it wouldn't be inexpensive). Duct sealing should be considered too.

- Except for those with solar panels or located in one of the few municipalities with lower than market electricity prices, electricity is quite expensive. Gas furnaces are far more cost effective to use in California for heating than heat pumps. In most populated areas, the heating season is short anyway.

Do you have south- or west-facing windows? Sunlight blasting through them can be a major source of discomfort. West-facing windows are particularly bad as sunlight can shine through them from noon until dusk. If windows are unshaded, consider adding awnings or window film. I have a skylight that made my condo unbearably hot until I applied low-SHGC window film to it. On the inside, cellular shades can help; I have them on my south-facing windows. Are you an SCE customer? Check its webpage (or that of your utility) for subsidies. My sister received astounding subsidies for new HVAC systems on a duplex she bought in Sacramento.

All of these thoughts are super helpful and give me a great place to start. Thank you for all your expertise!!

At the simplest level, yes, you can add an AC system to your existing system (or a new one). The main issues are:

Is there room for the coil on the furnace outlet?

Can you run refrigeratnt lines outside to a condenser?

Does the complex allow external condensers?

After that, it's all down to the individual situation and installation specifics. Get a couple of HVAC companies to come in and give you an estimate.