Is there an off the shelf tool that intergrates with email to provide stats on emails you are receiving for support purposes ?

Lots of groups working on it. None are particularly good, but I expect that will change in the next 6 months. Freshservice has a bot that isn't particularly bright but you load data, solutions and suggestions. Point a decent LLM at the data set and you could probably skip the load data section. Note it will require your solutions in text form on the tickets. So if you aren't doing that now you need to start.