I have 5 pinned tabs on both of my laptops and these obscure the real tabs I want to see on my phone. Could these be grouped in their own submenu or hidden by a config?

The ideal solution is not yet clear to me. we've had request for the complete opposite too. That is, some users have asked to see their pinned tabs at the top of their synced tabs. For example: https://twitter.com/programmer/status/966889594691059712 Perhaps adding the pinned tabs to the top by default AND adding an option to exclude them would cover most use cases. Hard to prioritize at this time though. I'll put this as a P3 for now but as we collect more feedback, we can then properly scope this.