How long do I have to wait for glue to dry before staining?
The answer to this generally is, it depends. All the local conditions and individual variables1 work together.
Because of the specifics of your build, with the plywood screwed together along with the screws, you can begin finishing much earlier than in other situations where you wouldn't want to remove clamps too early — here the screws are the clamps and they're permanently part of the structure, meaning the two sheets of ply glued together face to face can't move relative to each other.
I would caution that 30 minutes isn't a long enough wait. I'm sure many have done this bonding together plywood and other sheet goods and think everything has gone perfectly but it's much safer to leave it at least a couple of hours, and longer if it's cold.
Just to mention, the 24 hours quoted for the full drying time is really generous. Even in challenging conditions it would usually take far less time than this for you to be safe in assuming a glue joint is fully dry, perhaps 6-8 hours, although you could give yourself a safety margin and wait a full half day. Only when bonding two surfaces where one isn't bare wood (so therefore can't absorb water from the glue) would I wait 24 hours or longer, and even that may be excessively cautious.
Which leads on to my next point, erring on the side of caution. There's never a downside to waiting longer before disturbing glued pieces or putting them under light stress, while there most definitely is to not waiting long enough — removing clamps too early is likely one of the three most common causes of glue-line failures2.
1 The humidity and temperature, the MC of the wood being used, whether the surface of the wood is old or was refreshed, how much glue you apply and how much of it is squeezed out during clamping (bearing in mind screws don't apply very very high clamping pressure evenly across your sheets) and last but not least the exact glue you're using.
2 The others being not applying enough glue in the first place and waiting too long after applying glue to bring the two pieces together.