This gist is a guide for setting up a navigation bar (with working hamburger menu) and active link styling in Next.js 13.
(it assumes you have already installed version 13+ of Next.js)
Updating your navbar from a previous version of Next.js should be fairly straightforward - all queries that arise during this process should be directed to the (excellent) Next.js 13 beta docs.
I have used "TODO" markers to indicate the sections that require updates for your specific application.