There's a push and a poll model for home assistant sensors: https://developers.home-assistant.io/docs/integration_fetchi...
Pretty easy to set-up a webhook trigger for automations in home assistant as well: https://www.home-assistant.io/docs/automation/trigger/#webho...
I was thinking about ways for the app to receive webhooks, but being able to send webhooks is an even better idea! I'm going to start writing down some thoughts for creating generic webhook triggers. That should also work for zapier (and possibly IFTTT) as well.