Oak [0] is the go-to web framework in Deno ecosystem, it has Koa-like API. There's also Opine [1], Drash [2] and some other that are also highly spoken of by folks at the Discord. AFAIK Oak used native HTTP bindings since their inception (if you were running with --unstable flag); and now that API is stabilized it will use it by default.
As for the NextJS; there are also a projects that try to mimic its API like AlephJS [3] and Fresh [4].