[Replay] Read response body stream instead of `body.text()`

Currently, we use `await body.text()` to get the response body of a fetch request for replay, both to get the body content as well as to calculate the length of the body.

This has the problem that if the body is a continuous stream, this will never (or very late) resolve. We kind-of solved this recently at least insofar as that we abort after 500ms, but since we still called `await body.text()` before we'll continue to read from the stream, even if we are discarding it.

We should look into reading the stream manually instead of using `body.text()`, which would unlock us being able to stop reading it after some time. But this means we need to take care of text conversion in there ourselves.

Related to https://github.com/getsentry/sentry-javascript/issues/9616