One of the most frequent questions we get is: Why doesn't Tusky support push notifications?
Because pushing to devices would require us to use proprietary Google libraries and to run a relay server. But we want Tusky to be pure FOSS (free and open-source software) and don't want to send any data to Google so we decided not to implement push notifications at this time. We are researching other possibilities to make notifications faster though. https://github.com/tuskyapp/Tusky/issues/793