My resolved in its default configuration will try appending .local and search via mDNS if no results are found via the DHCP provided server. I believe macOS does the same.

Ping foo on my machine results in foo.local being successfully pinged. Your mileage may vary.

> would potentially use mDNS if you have a ping that does such a thing

It's not a feature of ping, it's a feature of the name resolution setup on your machine (nsswitch and/or resolved on Linux).

> Rather, most routers add DHCP hostname requests to the local DNS routes

What do you mean?