If you are developing the channel, the channel would need to be running/active on the client's roku. Then you could track who is logged in and try to send out remote input commands to trigger an event on the device like refreshing the content list and screens. https://sdkdocs.roku.com/display/sdkdoc/External+Control+API Your app could need to look for the custom events being sent to it from your server push.
If you are using Roku Global Search, last I heard was it updates the contents automatically every hour - so if you have a new item indexed in your search feed it will update on its own for that.
The only PUSH notifications Roku supports, without doing something like what I said, is for the Roku Billing system, and PUSH notifications for the Roku mobile app.
https://sdkdocs.roku.com/display/sdkdoc ... ifications
https://support.roku.com/article/115005 ... mobile-app
Yes, that is all there is, those are the only options.