Not the OP, but I can definitely relate. Pure IC roles terrify me. I've been CTO and Head of Engineering of several start-ups, also made some money when one sold — yeah, I'm a lot like the OP. But leetcode is deplorable to me, when I hire (which I've done plenty of) I never made candidates perform such nonsense.
Not wanting a pure IC role definitely doesn't mean you don't enjoy coding. It usually means you don't want to be stuck building things that are unimportant. When you're working at a company that's making mistakes and you've the experience to know better, it's painful just sitting idly by. I know a lot of people can switch off their care factor, but some of us can't.
For example, I love coding, in the past 3 months I built an unofficial companion app for The Bazaar, an upcoming game. I built a back-end (Next.js, Vercel, Cloudflare, Supabase, PSQL), front-end (React), insight platform, packaged Windows and macOS desktop apps (Electron), reverse engineered the game (C#/Unity) and its networking layer. I was processing 300,000 player events a day.
https://bizarre.gg/runs/00493ccf-5b96-523c-beb4-06e8154cc158 (view on desktop, click on the right)
https://bizarre.gg/meta
I was recently forced to shut down this project by the game company (as were other 3rd party devs working on stuff for the game). I was offered a role at the game company, which they reneged on at the last moment.
Perhaps because in my role acceptance email, I wrote about how I am keen to take ownership (in the accountability sense) and get involved with developer advocacy, tech blogs etc. I suspect this spooked them because they "don't hire beyond Senior", which is obviously an absurd practice that's typically put in place by inexperienced/insecure leadership. Typically companies justify this with "we promote within", which is a massive disservice to your staff, because it just means your staff never have access to mentors to help them grow.