I believe at this point dark mode should be treated as an accessibility feature and built right into browsers and css hints. Until that, just use DarkReader extension with suitable settings. It can change brightness, contrast, saturation and plays well with syntax coloring etc. Screws up only a few sites where you can turn it off on per-site basis. No in-site dark mode does that, and dark modes are often even more toxic than bright modes.
The reason why this is tricky to do is that websites have custom designs. It's not a trivial problem to make a dark mode version of the design. You can't just flip the colors. There are design work in making sure your design works well in both dark and light modes. Most automatic dark mode solutions don't usually work across the board.
I love dark mode... when it's dark! When my colleagues are using dark mode in a sunny and well-lit room, I'm thinking guys do you just really love squinting?
Judging by what I see at work, where people seem to use dark mode during daytime in teams, outlook and others, which isn’t the default AFAIK, I’d say quite a fair bit.
Someone has to develop and maintain it. It's difficult to quantify the development/datacenter efforts with respect to end user displays. I do doubt dark mode comes ahead at all at any rate. Morealso, OLED displays are overall ill-suited for regular work due to burn-in -- those are the only ones that 'can' save energy (unless you count CRT - but they would be way worse to begin with). The cost of the shorter lifespan OLED (burn-in) would heavily outweight the energy saved - you are looking at 15-20Wh top.
Note: displays with backlight (the extreme vast majority) display blacks by blocking the light, so the dark mode alone doesn't save anything. There are ones with local dimming that can partially benefit.
Local dimming is becoming more popular, OLED is improving, and MiniLED or whatever they call it will be viable one day.
Maybe you're right about that not offsetting whatever server costs though. I don't think "develop and maintain" affects the environment, but maybe OP was including human resources.