Good point about the "if it's a refund request, also..." lines being a second prompt in disguise. I'd add one step when splitting: write a tiny test set first. Pull five or six real support emails, including a refund, an angry one and a vague one, and run both new prompts on them before you retire the old one. It shows quickly whether the reply prompt lost anything.

For chaining, I like giving the first prompt a fixed output, e.g. "Return only: urgency (1-3), topic, one-line summary." Then the reply prompt starts with "Customer issue: [summary]. Urgency: [n]. Write a warm reply under 120 words, no promises about refund timing." Short hand-offs keep each half easy to debug.