I'm not super sure what you're complaining about with the navigation bar. It's well within the realm of what Google uses them for. Go look at the YouTube app for example. It has a button on the navigation bar that opens a bottom sheet as well. I'd argue Sync's use of it is more in-line with the guidelines than YouTube is, since the sheet for exploring is closer to a destination than a sheet for uploading different kinds of videos. The only odd thing is being able to convert the FAB into a navbar button, but at least it's an option and not a requirement.

YouTube Music and Google Podcasts also have an "Explore" option on the navbar, they just open a page instead of a bottom navigation. He probably could convert that sheet into a page to make it more consistent, but it's probably a sheet for usability reasons.

I think the point about the FAB is good in theory when talking about what the material guidelines say, but so few apps actually use the FAB, and I think Sync's implementation which allows for such robust customization is a good and fairly intuitive use of it, even if it doesn't exactly follow every guideline. It still does allow you to pick one primary action for it. It just also gives you more options.