Something I don’t understand is: why do we need to allow the user to explicitly set dark mode or light mode? Why can’t we just check prefers-color-scheme and leave it at that?
Because it turns out that while this might sound like the easy, simple, convenient, right thing to do, if you try it (as we did), what happens is that people will forget or not understand they set it, and be unhappy and complain: https://gwern.net/design-graveyard#auto-dark-mode
(You can do the fallback to the CSS prefers setting, to try to not break dark-mode users, but if at all possible, you do want some sort of widget or toggle - at least for now. I am hopeful that in maybe 5 years it can be removed and users assumed to understand it.)
Surely there is a browser plug-in that will allow you to prefer light mode for some sites and dark mode for others? Or even add a toggle to the browser UI?
I don’t see the value in having this implemented by individual websites.
Your average user wouldn't even know that there's a standard css property that a plugin could potentially control; though, yeah, it being a browser toggle would make it rather obvious (...assuming it's front-and-center somewhere, which is a rather high ask). Definitely won't find a location to place it that requires one click to toggle on mobile browsers, though.
Having the in-browser toggle would also be rather questionable for anything that has more than just "light" and "dark"; the options suck - either having the browser-based toggle be a "shortcut" for one toggle in your main theme settings (which likely means users are less likely to notice the full settings), or abandon the browser toggle entirely (which likely means a significant amount of users would assume there's no theming at all). And neither really fits for something that has, instead of just "dark" and "light", an additional "high-contrast" mode (which, depending on what the site's designers bothered to do, could be an extension of "dark", or a toggle combinable with either light or dark); so you'd want the browser-based toggle to be at least somewhat customizable. Also worth considering is that if there's some fixed set of things that the browser-level theme toggle can do, sites would be very heavily disincentivized from adding any other things as those would then require an entirely custom theming setting panel.
I'm exaggerating somewhat, sure, but I don't think you'll find any way to have a browser-level theme toggle that doesn't end up pretty bad in a significant number of cases.
I'm also part of multiple organizations (in different contexts, as a subcontractor at work I have two orgs to answer to, for instance). I use customized settings to distinguish Work A from Work B when accessing the same application but with different user accounts. Yeah, I prefer dark mode but I'll use light mode for my actual employer (used the least) if I don't have other customization options.
I prefer my OS in dark but every website in light, it's always a hassle when a website decides for me based on my OS setting which I wouldn't want to extend beyond the OS chrome.