>I'm searching for a simple, self-hosted chat system that allows me to host unlimited bots and send messages (with notifications) to my iPhone easily.

I do this with IRC. I used to have a blog post up about it, back when blogs weren't just training data providers for LLMs, but I'm afraid it's been deleted.

tl;dr IRC works great, but you need to wire up push notifications. For android I used pushbullet, for iOS I am still evaluating the alternatives but pushover looks okay. IRC itself is nice because the protocol is shit simple, to the point that if you can type fast enough to respond to the pingpongs you can cosplay as a bot using nothing but telnet. As a text protocol it's easy to inspect and doesn't require binary decoding of packets for debugging.

I recommend the Ergo ircd. It ships as a single binary (golang), can support tens of thousands of clients, is at the forefront of the ircv3 modernization initiative, and is under active development.