I have done this with React apps using express. But never with Next. At first it looks like it would be possible with multi-zone in Next but that doesn't seem to do the job. So my other recommendation would be to try to use a docs.domain.com instead and host it separately. Then you have a /docs url or a button that redirects to the doc domain instead.
Firebase has free hosting and allows you to setup multiple sites. So it should be fast to test this setup there
I'm going to actively try to get this to work with Next myself but I do not think it will work because of how they are developed. So I would do the above recommendation and if I find a workaround, I'll post an update.