This is a split bus aka rule-of-six panel. They were originally developed because breakers over 60A were cost prohibitive (no longer true). They are outlawed now, and are dangerous because nothing prevents you from overloading the service.
They were allowed when a load calculation was done that showed the house would not overload the service; however, when people add circuits they don't bother to do another load calculation, and that's the danger. Normally a large load like the A/C would be put in the Rule of Six area; putting it in the Lighting area makes me wonder if they did a load calc and it went badly. Any idea what came out of that space?
GE and their double-stuff rejection system
GE has a funny way of doing double-stuff breakers. All their bus stabs look like normal bus stabs, a flat horizontal blade maybe 3/8" to 1/2" wide. However, on spaces enabled for double-stuff breakers, they have a vertical rod - I call it a "cruciform" for the way it crosses the bus stab. The double-stuff (1/2" wide single and 1" wide 2-pole) clip onto this cruciform.
In 1966 NEC added "CTL" rules limiting the number of double-stuffs in a panel. They required mechanical keying to reject double-stuffs where not allowed, so most builders notched their bus-bars and came out with "CTL" breakers which would reject in a normal space. (as well as non-CTL breakers to support pre-1966 panels, haha, guess what everyone did). GE simply omits the cruciform. Which means, there's no way to trick a double-stuff where GE doesn't allow it.
In a split-bus aka "Rule of Six" panel, there can only be six breaker throws to de-energize the whole panel. So there would be no earthly reason for GE to install the double-stuff-enabling cruciform in those spaces.
Now, this panel only supports four full-size 2-pole breakers in the "Rule of Six" section. You might think GE intends you to use three 1" wide 2-pole breakers per side. Looking closely, it appears the cruciforms are in exactly the right place to support just that - note there is no cruciform on the top half of the top space, so you can't put a 1/2" wide 1-pole there. You'd have to leave that empty.
You can't run 2 120V circuits out to a shed, anyway
Rule 225.30 says you can only run one circuit to an outbuilding. The rule intends that be a feeder to a subpanel. However, there are certain exceptions:
- A different-voltage circuit is OK, and this is where I'll introduce you to the multi-wire branch circuit. This is a 120/240V circuit with 120V loads placed between one of the two hots and the shared neutral. You can also power 240V loads between the two hots (but the breaker must be 2-pole if you do that).
- If one of the circuits is switched from the supply end, then it's OK. So if you are hellbound and determined to have 2 independent circuits, find a believable pretense to put a switch on one. (e.g. so you don't have to put your shoes back on to switch off the forgotten shed lights).
One option is to get a full-size 2-pole 30A breaker, place it in the open position, and use it for the A/C. This will require extending the A/C cables, but you can do that with normal (well, large red or tan) wire nuts.
That frees up the 2 double-stuff spaces for 2 thin breakers (or a 20A 2-pole for an MWBC).
Another option is just get two full-size 1-pole 20A breakers and put them in the Rule of Six area and use them for your new circuits. You still only have five throws to turn everything off, so that's legit. Nowhere is it written that circuits in the Rule of Six area must be 240V.
You could also get one 1/2" and one full-size breaker in that Rule of Six area, if that matches the current knockouts that are removed from the panel cover.
For that matter, you could put three 1/2" breakers in the Rule of Six area, because that will be only six throws. Keep in mind for future, heh, expansion in this very full and obsolete/dangerous panel.
Any now-empty breaker knockouts need to be filled with a blanking plate - you can't have curious fingers finding bus bars. I find those blanking plates to be expensive, hard to find and very flimsy - so I prefer to arrange panels so all holes are full of real breakers. Which are not flimsy.