I’m sharing most of your struggle too, maybe besides the BibTeX as I’m not into the research field myself. Great insight. The ones that hit home the most for me is the “fighting with editor”, “side by side pane” (there is an issue on this from March), and the inline sets.
I’m thinking an easy way to enable notifications would be to support any push service, for example, “pushover”. This is an excellent service I’m using for tons of other things.
More importantly, having a system of plugins through scripting would allow us to write some simple code to interact with various APIs. We could even handle the notification push ourselves that way.
I will continue using Anytype, though, enjoying it so far.