For embedded systems probably just... allow users to read the metrics easily and let them implement what they need using the method of pushing they use. use-cases will probably be different enough that they'd need to customize it anyway.

Most would probably end up as pushing metrics via... something (MQTT?) to gateway that will push it to their metrics system.

Pulling/polling metrics honestly is pretty bad idea most of the time. It makes it easy to implement ("just* provide a web page with metrics) and allows poller to control intervals (which is only a problem if your configuration management isn't up to snuff), but complicates a lot, now you need to setup whole endpoint discovery instead of just saying "hey, apps, here is URL to push your metrics to, have fun".

We for long (10+ year) have system based on collectd and it's line protocol, and while it have some drawbacks (no tags, just rigid structure with host->plugin->plugin_instance->type_type instance, works well most of the time but 100% of the time), push nature is very light on resources (it's just an UDP packet full of metrics, no need to setup whole TCP connection, doesn't even need bidirectional firewall)