But reading your description, I'm left slightly envious and pondering how vim could be integrated better with a browser with web development in mind specifically. I'm not sure what it'd be but it gets me thinking :)
I switch between the two easily enough but I often have to click somewhere to activate the browser part or DevTools. Switching between tabs in devtools is also inconvenient. So that makes me think of a custom app with vim bindings integrating vim, the browser itself and its developer tools... Sadly I'm afraid that would be a huge amount of work in languages I don't know to get that going. Still, thanks for making me think about it!