You are aware that 'local-first' does not mean 'no-network'. Having a sync mechanism that runs in the background without user notification can be quite disconcerting.
I mean, I did it, I built an app with a transparent background sync. Then I added a special page, 'sync center'.
In reality, mobile devices don't always have perfect network connections. Therefore, when the user is unsure whether the device is in sync or if the sync is in progress but encounters an obstacle, they might perceive the app as unreliable.
Banning spinners is dogmatic, not user-centric.