I’ve setup sway following the wiki. (Not using home manager for sway). I have implemented the theme options documented there. I also watched the vimjoyer YouTube video on theming and added that as well.
But I’m still getting white menu items (using a dark theme) on my apps.
This kind of thing can usually be diagnosed using strace to see what themes the app is searching for and where. That is a good place to start if you haven’t tried that yet