I'm making focaccia but this probably applies to any bread/dough.
Does resting the dough in a deep bowl give a better/worse rise than a flatter dish (e.g: a tray dish you'd use to actually bake the thing).
I have this deep, V-shaped baking bowl with steep sides. My theory is that a deeper container allows for a better rise since there's more dough in the vertical axis. The walls also might support the dough better.
The purpose of the first rise is to let the yeast fully activate, gluten to develop and expand the dough as the yeast ferments sugars. If you do it long and slow in the fridge you'll get some flavor development as well.
There's very little difference in using a bowl over a tray, all those processes work regardless. You may see a bit less lift in a bowl over a tray because there's more weight on top of the dough at the bottom of the bowl, however once you move it to your baking dish or tray it's going to bounce back so you won't notice a difference in the end.
You want to handle focaccia, ciabatta and other very high hydration doughs as little as you can because you are trying to get as light a structure as possible. Proofing focaccia in a bowl and then transferring it to a dish just knocks air out of it, although you'll get most of it back in the second rise. You can get maximum air by proofing it in the dish or pan it's going to be baked in, and save yourself the hassle of moving it at the same time.
With doughs you have to shape you're going to lose some air, some need to be worked a bit before the second rise to ensure consistency, in either case bowl or tray makes no difference.
