Where can I see every order the apps have sent me today in one place?

Two places. Orders from the apps on Settings → Delivery apps lists the last forty with their state, which app they came from and what happened. The orders board shows them among your own orders, and the line names the app. For a day's total, they are ordinary orders, so your dashboard and your monthly statement count them too. The Orders from delivery apps tab in the docs explains where app orders appear.