I don't think the screening process at the theater would be more complicated than it already is. I've seen four Broadway shows since the reopening, and the entry process for all of them has been relatively smooth and quick (pro tip for Harry Potter: enter on 42nd Street). These additional steps shouldn't be too onerous.
In terms of checking for the booster, it's a flash of your vax card (and I think most of us are using one of the apps on our phone), where what they're looking for primarily is the latest date (which is prominently featured on the NYC Covid Safe app); if it's within 6 months, you're good to enter. I think the logistics of asking everyone to do a 24-hour test are untenable in this country because of the scarcity of affordable rapid tests, but checking the results shouldn't add too much time to the entry process, especially if that also gets built into the NYC Covid Safe app and the like.
