I see, thank you for the suggestions.
I just tried it with a different theme (Minimal) and with none, and I observe the same switching. If I am in Light mode on the OS and I switch to Dark in the Obsidian settings, it goes Dark of course. But if I quit and reopen Obsidian it opens in the Light version of Minimal. (Same works in opposite direction if the OS is Dark and I set the theme to the Light). So it’s not the particular theme.
I’m not on the Monterey beta, so it could be that upgrading would fix, though I’m not brave enough on my main machine.
In the meantime I have chomped away at the Pisum CSS code to make all reference to dark and light the same. I probably broke something, but now my Light mode looks like a Dark mode. The silly thing is that the Pisum CSS doesn’t have an actual Light or Dark, it switches to the Andy sliding panes thing in the Light mode, which I can’t be doing with.