True, there’s no native integration between Facebook and Hospitable. But if I got it right, you can Connect Another Tool > Website Link > Paste your Hospitable Direct booking URL. So basically you can redirect it to your Direct page.
Only missed point is that “BOOK NOW” CTA wouldn’t be available without an app your limited to “LEARN MORE” which won’t get so much activity…. It’s also potentially a place to stand out as a PMS as people see the hospitable come up there on a competitor's page and want to use the same PMS ect