I was CTO of a <20 person startup. I recruited the entire tech team, collaborated with the CEO to build the product backlog and spec things out, presented to investors, but also had at least 50% time to code. Not all “CTO” roles are the same. At a small company they better be hands on.

It's very common to see a VP of Engineering managing the day-to-day operations while the CTO acts in a capacity like this.

You're saying "usually" about something that has definitely not been a norm in my career. It seems like there's really only two ways to interpret that arrangement: either the CTO is in fact the EVP/E (fair enough! lots of CTOs are other exec roles with a funny hat), or the CTO has a single top-level manager report, in which case what really happened is that the org hired a pro to run engineering and put the "CTO" out to pasture.