A while ago, I made something exactly like this called writedown: https://writedown.app
It is a free and open source, simple and easy to use Notion alternative.
I had to leave it midway (it's ready to use and stable though) because my other projects needed attention but I'll get back to it someday :)
1. The site was shown in a light-theme version and the sun icon on the upper-right corner. 2. When clicked on the sun, it changed to a moon icon but nothing else changed, the light theme was still on. 3. When clicked again, the moon changed to the sun but this time the dark-theme was engaged. The only issue is that the dark theme is displayed but the sun icon appears. 4. When the sun icon is clicked, the light theme is engaged and the icon changes to the moon.
For some reason it feels counterintuitive. Just sharing for reference but great site!
We're actually in the process of changing the whole landing page and updating the app, so hopefully it will be stable enough soon :)