Add Pushover as a push target so when you click share on Android you can select the app. It would also be great if you could select a specific app such as iOS, desktop, or even another group. 

If Android notifications contained the options to "Delete" or "Mark read" instead of just clicking on the message to open the app, you could quickly triage messages dismissing not so important ones. This would also add the ability to interact to some degree with the notifications from Wear OS as well as the lock screen or with notification mirroring in ChromeOS or Windows 10.

Please consider adding heartbeat functionality for Teams accounts.

This would, IMHO bring you up the next level of robustness needed for some businesss.

Simply you provide a 'heartbeat' url, which your customer polls every say, one minute, if the url has not been accessed in five minutes, a message or SMS is sent warning the user the heartbeat has expired, and their monitoring system may be down.

A new Section in the left panel called "Favorites" / "Important" / "Pin" message.

Each message will have an icon to mark it or slide action.

The reason is to easily read important message, and not scroll until I find the one I want to make an action or Search by text.

Will there be a macOS Catalina official Pushover client now that Catalyst makes it easy to convert an iOS app into a macOS app? This would be awesome considering both unofficial Pushover desktop apps are now unmaintained.

It would be great if the Pushover app for Android would be extended to support Wear OS and hence be possible to install it on Wear OS watches. This would make it easier to interact with the app.