Too many forks, each with its own enhancements... If the purpose of this one is just a single feature, why not contribute it to another popular fork?
F-Droid
F-Droid is an installable catalogue of FOSS (Free and Open Source Software) applications for the Android platform. The client makes it easy to browse, install, and keep track of updates on your device.
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UnifiedPush is a key feature and not the only one. You can read more about it on its github repository: https://github.com/drizzt/Mercurygram
UnifiedPush was suggested to Telegram FOSS about 2 years ago. But it didn't happen until now: https://github.com/Telegram-FOSS-Team/Telegram-FOSS/issues/577
There are also forkgram, nekogram x, whatevergram... I use negkogram x, in particular, and I don't want to switch to another fork to get unified push but losing other features. I guess forkgram users also stick to its features. Etc.
Never heard of unifiedPush, but looks great. Is it becoming standard for self hosted push notifications? I need to take control of my own notifications...
Ntfy is pretty standard, so... Yes. It's an implementation of this specification.
Ntfy is pretty common