Also, one of our main USP is the ability to take action on any notification. Slack provides a strong api layer to pull this off, while its extremely tough to do the same as a gmail app. Chrome extension is still a viable option, but for now, we chose to go ahead with Slack due to the collaboration element.
Regarding the engineering manager usecase, although we don't have deep relevant integrations yet, we are considering adding support for Jira, Trello and Sheets as well, but would love to know if any of that will be as helpful in your day to day work. We are not venturing into tech alerts yet, as there are good comprehensive solutions already in place but would love to know of any gaps that might exist where a configurable action layer would be helpful.
Jira is the only tool I use that you mentioned, and as far as that goes, I'm not really sure what I'd take action on. I get a bunch of notifications about ticket updates, but I mostly ignore those. The one thing that would be pretty awesome -- which I think Atlassian already does, we just don't have it configured at my company -- is to be able to respond to comments from Slack.
This seems really cool. As an engineering manager, I can't see how I'd make use of this in my day-to-day, but I could definitely see the sales team using it.
One of my biggest questions is: why Slack? It seems like the majority of the incoming streams would come from email. And it seems like you're targeting integration with SalesForce -- at least that's what I get from the home page.
Other than that -- not to nitpick, but there's a grammar error in your first graphic: https://www.tryscribe.com/static/img/email.png . It says "You've have an email".