I don’t use browser private/incognito modes very often, but sometimes when I do I also want some of the installed Extensions to be available. My browser of choice is Vivaldi and it does allow you to enable extensions, on a per extension basis, in private mode.
To do this, open the Extensions page from the menu or using
Ctrl+Shift+E and click the details button on the plugin you want to enable in private mode.
At the bottom of the window which opens, click the Allow in incognito toggle to enable:
The next private window you open will have the extension enabled.