What does "waking up to something" mean?
"Wake up to something" in this context refers to something you encounter right after you wake up. Here, "Waking up to an inbox three times fuller than normal" refers to seeing three times more emails than usual (that have accumulated overnight) when you check your email after waking up. Ex: I woke up to rain when I looked out my window this morning. Ex: I woke up to a fever and headache, I'm not coming to work today.