Sadly, it doesn't help.
I think I was fixing this or similar issues before, and I was able to fix some of them by using the "Preferences" and "Secure Preferences" files in the "Default" folder in the main profile.
And those things works great, but only during development when I load the extension with web-ext.
Somehow when Pupeteer starts it, this specific modal setting is reset or not set or something... but all the other settings like where on the screen should the Chrome start works fine.
I think Pupeteer "installs" the extension which resets the option but web-ext loads it instead. (just guessing here of course)