I would love a (local!) solution that will process my emails and chat messages on umpteenth platforms and split them somewhere by project or even more granular topics, including generating TODOs.
Back on the topic at hand, the people who used to send you emails must be very organized, because mine always include multiple TODOs that need to get split anyway.
I'm afraid I've always been maintaining my own private notes and todos at all jobs.
Copy / paste is your friend in this case.
(And yes, I'm generalizing and you can make these apps into things they are not. But life is better if you don't.)