Chat that only admin can post to?

As a workaround for the fact that we can’t do push notifications, I wanted to use the chat feature for alerts/notifications, so I want all users to be able to see the chats, but I want ONLY me to be able to post them. Is that possible?

Short answer: No.

The native chat tab has very limited functionality, and you can’t control who can post messages. It’s either all or none. You can conditionally hide the tab, but I don’t think that helps your use case.

It sounds like you need some sort of announcement feature, where everybody can read messages, but only privileged users can post. It wouldn’t be too difficult to create this. It’s really just another table with a few controls over editing.