At the start of Seam, we spent a lot of time reading those specs and absorbing some of the key ideas expressing in its core documents. As a result, you'll see a lot of W3C WoT terminology throughout our API and its docs ("capabilities", "events, properties, actions", "affordances"...etc). My mom (of all people!) is the one who pushed us to really spend time in those docs and understand where the designs were coming from.
I think ultimately we began diverging a bit from those specs when it came time to solve customer needs, such as device-category standardization, async handling of access codes...etc. But I have fond memories of going over those docs with my mom, highlighting certain passages of their docs on paper printouts, and debating the merits of different approaches.
Also feel free to ping me sy@seam.co if you guys need help with various integrations.