No worries about the multiple posts, happens a lot with new members so just a heads up.
BBs are one of the most annoying things to get right. All the cranks you list require a different one and it can even differ depending on models for some!
Starting with the frame, it’s almost certainly an English thread. That means all the common threaded BBs will fit fine. Specialized call all their BB shells OSBB so it can get confusing, but as they have inserted a threaded adapter I’m almost certain it’ll be a standard 68mm shell so you can run the common cranks you would want on the track. It would be really strange if it wasn’t.
The Miche pistard and air cranks use a 24mm external BB, so theoretically any BB that works with Shimano Hollowtech2 cranks will work. However, I know someone who runs these cranks and they said the Miche BB works better. These cranks and the Omniums have the axle attached to the crank, so you can’t buy the wrong length BB axle as they are just cups.
The Sugino messenger uses a JIS Square taper and needs a 103mm axle for the correct chain line. Any 68mm shell BB with those specs will work. Sealed isn’t necessary for track. These cranks are ok, but they ain’t 75s and if you were thinking of upgrading in the future you’d have to replace the BB too as the 75s have a specific taper.
Sram Omniums use a GXP BB, which is similar to Hollowtech2, but the cups reduce from 24mm to 22mm so you need a specific GXP BB. I run Omniums on my fixed gear in summer (which is short in Scotland!) They’d be my choice of the ones you list. Nice and stiff, easy to fit with a 10 and 8mm Allen key and the BBs are light and cheap (although as it’s for the track you won’t need to replace it often).
Current Dura Ace, 7710, use octalink BBs. I’m not a fan of these cranks. The 7600 were better and used a JIS Square taper, but fixie kids have pushed up the price in the second hand market to crazy money.
TL : DR - Get 165mm Omniums. The BB is a 68mm shell threaded GXP, think it’s called the team GXP or something like that.