What's happened here is precisely why
communication should be public, it's revealed a real problem in the company you're at.
I've been on teams exactly like this, but the problem isn't public channels, it's "leadership" not knowing how to let go and trust their teams. Doing more work in private is the negative consequence of this bad practice, but I assure you this issue will eventually cause problems no matter how clever people are in avoiding public conversations.
And startups that are on the path to long term success will have leadership abandon this type of butting into every day communication very early in their growth. A good C-level must learn the build teams that can scale beyond their individual interventions. You literally cannot grow beyond a 30 person organization (and survive) if this much intervention is required.