The Librem 13 has yet to see official Coreboot (or Libreboot, the downstream of Coreboot without any firmware blobs) support by Purism, which has ticked off Coreboot developers before in posts like
The truth about Purism: Why Librem is not the same as libre and The truth about Purism: Behind the (coreboot) scenes. There have also been guest posts on Phoronix regarding the topic, such as Purism Librem 13 Funded, But Will Likely Fail To Provide Freedom & Privacy.
Now there is upstream Librem 13 Coreboot support pending, but it wasn't done by the company. Coreboot took to Twitter today and announced, "Hey [Purism]! Will you throw a party for [a Google developer] for doing the coreboot port for you?" There was also a second tweet taunting Purism over this port, but that was since removed.
Duncan Laurie of Google has published Librem 13 support for Coreboot, a port he did on his own. The port allows for Coreboot to boot the Librem 13 with Coreboot. However, it's not fully-open but relies upon the Intel firmware blobs, as is sadly the case for all recent generations of Intel processors.
All major functionality should be working with this Librem 13 Coreboot port while Duncan had to extract the VGA BIOS, management engine, and Intel firmware descriptor from Librem 13's blobbed-up BIOS. He also copied over the memory initialization and silicion initialization binary blobs from a Broadwell Chromebook BIOS.
It will be interesting to see if Purism makes use of this Coreboot port in future revisions of their Librem laptop.