Support real HTTP requests when using an `http.Handler`

The assumption is, that the web server under test serves all content locally, including 3rd party libraries, like HTMX or React.

When the browser is constructed to call into an `http.Handler` directly, it will not make _any_ real HTTP requests, so any application that references scripts through CDN will not work.

**Shout out** if this affects you. It's a simple problem to solve, just wasn't prioritized.

Start by tracing how the browser is constructed with an http.Handler and how requests are routed in the Go codebase. Verify the current behavior with an application that references HTMX or React from a CDN; the work is done when those external scripts can load through real HTTP requests while handler-served content continues to work.

Written by the indexing model from the issue text.