It hardly makes a difference on LCD monitors. See also blackle
Edit (25 minutes later): a phone screen seems to use about 1W more on a white background than a very dark one from what I could quickly find on mobile (https://www.xda-developers.com/amoled-black-vs-gray-dark-mod...). 5 billion people seem to use phones for some 4.4h/day (https://backlinko.com/smartphone-usage-statistics). Assuming 70% uses OLED worldwide (probably much less, but I can't quickly find a source for this) and 50% of the time is spent on reading text (not tiktok videos or whatever, where you can't use dark theme), that's 2.8 TWh per year. About 178'000 TWh of energy are used by the world per year (https://ourworldindata.org/energy-production-consumption).
So this should save 0.002% in this best-case scenario where every text-based application switches to nearly black backgrounds and most people have OLED screens and people actually use their device for text at least as much as for media consumption.
Is that worth it? Maybe, but perhaps not as effective as not loading megabytes of JavaScript on every page, not downloading ads and tracking on every page, and funding low-carbon electricity generation needed for your systems. Wikipedia already is pretty good on the first two afaik, the latter I can't easily tell beyond saying in 2019 they're doing a "best effort" in buying green-labeled electricity and making an inventory of other emissions like plane travel (https://wikimediafoundation.org/news/2019/09/19/how-the-wiki...)
Edit (25 minutes later): a phone screen seems to use about 1W more on a white background than a very dark one from what I could quickly find on mobile (https://www.xda-developers.com/amoled-black-vs-gray-dark-mod...). 5 billion people seem to use phones for some 4.4h/day (https://backlinko.com/smartphone-usage-statistics). Assuming 70% uses OLED worldwide (probably much less, but I can't quickly find a source for this) and 50% of the time is spent on reading text (not tiktok videos or whatever, where you can't use dark theme), that's 2.8 TWh per year. About 178'000 TWh of energy are used by the world per year (https://ourworldindata.org/energy-production-consumption).
So this should save 0.002% in this best-case scenario where every text-based application switches to nearly black backgrounds and most people have OLED screens and people actually use their device for text at least as much as for media consumption.
Is that worth it? Maybe, but perhaps not as effective as not loading megabytes of JavaScript on every page, not downloading ads and tracking on every page, and funding low-carbon electricity generation needed for your systems. Wikipedia already is pretty good on the first two afaik, the latter I can't easily tell beyond saying in 2019 they're doing a "best effort" in buying green-labeled electricity and making an inventory of other emissions like plane travel (https://wikimediafoundation.org/news/2019/09/19/how-the-wiki...)