The fire-fighting thing sticks out to me a bit, in part because it's caused me pain in the past and in part because you keep mentioning it. I might venture a guess that one of the underlying issues that's really getting to you is not the lack of actually writing code, per se, but that you have always had environments where you can get lost in deep focus or flow, and now your brain is being actively rewired to support continual rapid context switching. This is uncomfortable and unfamiliar and your brain is rebelling against this new environment.
I've never had a CTO title, but I've been in many similar positions.
In case you decide to stick it out for a while, I would suggest several easily implemented opportunities immediately:
(1) Establish an #engineering-support channel in Slack and a Triage calendar in Google Calendar. Put your team members on a rotating schedule to triage any engineering fires that the business has.
The Calendar should pipe into the Slack channel at 9 am every day. For a few weeks, send an "@channel please remember $engineer is your point of contact for today." By then the rest of the business should get the idea. Instruct your team that you trust them to decide which issues need to be addressed immediately and which ones need to go into the queue, but if they have any questions they can escalate to you. Also explain you understand that context switches are expensive, and you are totally okay if this causes a productivity hit on their given triage day.
It doesn't mean you won't be interrupted with real fires, but it does keep the less urgent ones from creating a context switch for you. Include yourself in the schedule, and you can send the message to your team "we're all in this together" instead of "hey I'm too good for this nonsense."
(2) The Business guys will respect your calendar, and if they don't, you have leverage to call them out on it because The Calendar is sacred in the business world. Block out 2 or 3 hour chunks throughout your week to work on hard problems. You drive a lot more value this way than with the fire fighting, anyway.
(3) The Calendar also works for time with your family. Daughter's Ballerina Recital? Block out 4pm-8pm on your calendar as soon as your hear about it—"Blocked—At Home"—and again, leverage if somebody wants to interrupt you with a fire.
(4) Train everyone on how to add each others' calendar to their own calendar view; this seems obvious to engineering, but less engineering-minded people may not know they can do that.
I've never had a CTO title, but I've been in many similar positions.
In case you decide to stick it out for a while, I would suggest several easily implemented opportunities immediately:
(1) Establish an #engineering-support channel in Slack and a Triage calendar in Google Calendar. Put your team members on a rotating schedule to triage any engineering fires that the business has.
The Calendar should pipe into the Slack channel at 9 am every day. For a few weeks, send an "@channel please remember $engineer is your point of contact for today." By then the rest of the business should get the idea. Instruct your team that you trust them to decide which issues need to be addressed immediately and which ones need to go into the queue, but if they have any questions they can escalate to you. Also explain you understand that context switches are expensive, and you are totally okay if this causes a productivity hit on their given triage day.
It doesn't mean you won't be interrupted with real fires, but it does keep the less urgent ones from creating a context switch for you. Include yourself in the schedule, and you can send the message to your team "we're all in this together" instead of "hey I'm too good for this nonsense."
(2) The Business guys will respect your calendar, and if they don't, you have leverage to call them out on it because The Calendar is sacred in the business world. Block out 2 or 3 hour chunks throughout your week to work on hard problems. You drive a lot more value this way than with the fire fighting, anyway.
(3) The Calendar also works for time with your family. Daughter's Ballerina Recital? Block out 4pm-8pm on your calendar as soon as your hear about it—"Blocked—At Home"—and again, leverage if somebody wants to interrupt you with a fire.
(4) Train everyone on how to add each others' calendar to their own calendar view; this seems obvious to engineering, but less engineering-minded people may not know they can do that.