[11.x] Add middleware before sending request and dispatching events

[eduance]

Backstory
See my comment.

Problem

The problem is that we currently do not initialise the middleware before sending the request which causes an issue further described in #51980.

Http::globalRequestMiddleware(fn ($request) => $request->withHeader(
    'User-Agent', 'Example Application/1.0'
));

Solution
We should always first add the middleware to the stack and then build any follow-up handler.

This now causes our middleware to be initialised at the right time and the user-agent is now correctly set when listening to the RequestSending event.

Please let me know if there is a way I could improve this test! :)