Does Cribl Edge send any sort of heartbeat?

Edge Nodes will periodically (every 10 seconds) send a heartbeat to the Leader. This heartbeat includes information about themselves, and a set of current system metrics. The heartbeat payload includes facts – such as hostname, IP address, GUID, tags, environment variables, current software/configuration version, etc. – that the Leader tracks with the connection.

Managing Edge Nodes | Cribl Docs

If you have an Enterprise or Standard license, clicking the left nav's Edge Nodes tab opens a Manage Edge Nodes page with two upper tabs: Nodes and Mappings.

The System Metrics source is enabled by default for Edge nodes and can be added in Stream Worker nodes too if desired. It emits periodic (every 10 secs by default) events that contain various performance metrics for the host; i.e.node_uptime_seconds. You could monitor those metrics downstream in Splunk or other destinations to track the nodes availability.