I have some advice, but I’m not sure how close it’ll be to what you’re looking for.
It sounds like the email from the client triggered work for you, are you saying you need input from the designer/PM to do that work? Need more info from the client?
If that’s the case, this sounds like a follow-up type task to me. These come up for me all the time. You’ve done what you can but the task is basically blocked and can’t be completed without work/input from other people outside your control. It sounds to me like the problem is you still own the task but are blocked.
The way I handle this is by adding some kind of status to the task showing it is blocked (In my case I move it to a Blocked column and add one of a several different Blocked tags denoting the type of block [internal, vendor, client]). Typically I put a brief comment in stating why it’s blocked and how it can move forward so people reviewing it know. I might paste the email in (more about this below). Then I’ll create a second “follow-up” task (there’s a feature for this in hacks) for myself with a due date an acceptable period out in the future to remind me. I mark the task for “Later” so it’s not showing up in My Tasks in a pressing way, and basically forget about it. At this point either the people get back to me before the follow-up task comes due, or the task shows up back in My Tasks in Today. If it’s back in Today, my comment in the task reminds me what I needed to unblock it and all I need to do is ping someone and say “hey, haven’t heard from you…” and repeat the process. I also put all these follow-up type tasks in a special private project so I can see how much stuff I have out there as a time-bomb. I put all my communication in the follow-up task and can also easily see if no one is responding and take appropriate action, etc.
With respect to your email question, I don’t email to Asana all that much. I tend to prefer my own formatting to what an email comes in looking like. I write a quick summary of the email in bold and underlined and then paste in the email:
I found this ends up being faster and more helpful despite it’s “manual-ness” because if I can’t summarize what an email is saying, I generally find I didn’t read it well enough. It also helps me avoid a lot of re-reading when I go back and research a task because I took the time to distill it down to what matters to me and my team.
Hopefully there’s something helpful in here.