Tag incoming messages by what they actually need
Not every client message needs the same kind of attention. A billing question, a general check-in, and an urgent problem all arrive looking similar in an inbox, but they deserve very different response speeds and often different people handling them entirely.
Sorting messages by what they actually need, rather than treating every single one as equally urgent, saves you from either rushing routine questions or letting real problems sit too long without notice. Even a rough system — urgent, routine, informational — makes a real difference once you start using it consistently.
You don't need anything complicated to start. I started with just three categories myself, and that alone caught most of what actually mattered. A short set of rules or keywords that route messages into these categories is enough to get the sorting mostly right, and you can refine it as you notice what slips through the cracks.
Try this today: look at the last stretch of client messages you received and sort them into a few simple categories by what they actually needed from you.