As the standard says, DATA0/1 are used for error checking. After the bus reset or SETUP transfer (and a few other cases too), toggle bit resets to 0. And it toggles with each frame sent by either side. Both host and device keep track of this bit. If a frame went missing, then either side would be able to detect it.
If I understand correctly what you mean by brackets, then it is just a request and response. For the request part of the SETUP transfer host will always send DATA0. Device will respond with its current toggle state. The fact that it is DATA1 here is just a coincidence. Although I'm actually not 100% sure, setup might reset the toggle both for both directions for the control endpoint. I'm too tired to check the spec.
Ok, yes, DATA stage of the control transfer would always start with DATA1, and setup stage with DATA0. As usual, control endpoint is not like other endpoints and does its own thing.
Section 8.6 "Data Toggle Synchronization and Retry" describes this part and shows examples of how error recovery works using those toggle bits.
Note that toggle bits are separate for the host and device (and generally they are separate for each endpoint/pipe), so both devices need to keep track of both bits - own and from the other side. And again, the algorithms of how they are reset and toggled are described in the spec.