One test is if the valve is out of the cylinder, is that a U.S. quarter coin will fit through the 3/4 NPS cylinder neck opening but will not fit through the 7/8 UNF opening, as the 3/4 NPS is larger.
Perhaps you already looked, but my Air Venturi SCBA 74cf specs the thread size on the label. My Brancato tank has a mesh net on it making it difficult read and is a pain to remove boot and net.
I did a fairly good search for Omega info and came up empty. PA doesn’t appear to carry Omega products. You might contact a vendor that carries Omega and see if their willing to share the thread size. Do you by chance have a pair of dial calipers where you can measure the ID of your tanks threads?
If it's made by Inocom like AOA picture then all bets are off. They will thread them any way you like. Paintball companies buy 5/8, pcp guys usually buy metric, but AOA can have them made for whatever valves they have on hand. Likely same as their bigger tanks. If it's not on the label, measure or call AoA