An update to what I am seeing. First, the behavior seems to have changed since I originally posted here. So this is what I am seeing now.
If I have "High priority notifications" enabled, I get a notification card displayed on the watch. It remains displayed until I clear it, either by swiping it away or clearing it on the phone, or another high priority notification shows on top. The bottom line is that I can clear the notification. If I do not have "High priority notifications" enabled, then the notification does not show. I must slide up the notification drawer to see it. This is the part that changed between AW 1.5 and AW 2.0. In the earlier version, the notification would appear for a few seconds, and then slide away. In the newer version, it does not show at all. This is not unique to AquaMail, as Gmail behaves the same way. So I blame this on AW 2.0. I prefer the earlier method, as I can glance at the notification when it occurs and decide what to do.
As for the other problem, when I read a message on my tablet, I get a new notification on the watch, it seems to not be consistent. I have tried turning off "Only when there are changes" with no effect. I have tried turning off "Only when new messages arrive" with no effect. I normally have both of these turned on. I believe that is the default setting. But the end result is not consistent. Sometimes reading a message on the tablet will cause a new notification, sometimes it will not. I have not been able to identify what the circumstances are for either situation.
My compromise is to first turn off "high priority notifications" in the global settings, and turn it on only for the account which is for work. I am grateful that this option is available in the account settings. I then use Tasker with plugins for AquaMail and AutoWear to generate more specific notifications as email arrives from people in my contacts. It's not perfect, but it will do for now.
One question about "high priority notifications". I could probably test this, but I haven't done so, yet. If an email arrives with the high priority flag set, will the notification act as though the "high prioriy notifications" option is set? I'm not certain I can take advantage of this, but it could be very useful if it does work this way.
I have only had the watch for about two weeks, so I am quite certain I will make adjustments to this process over time.