Prior to this commit, the `HttpTraceWebFilter` would collect the
response information (status and headers) for tracing purposes, after
the handling chain is done with the exchange - inside a
`doAfterSuccessOrError`.

Once the handler has processed the exchange, there is no strong
guarantee about the HTTP resources being still present. Depending on the
web server implementation, HTTP resources (including HTTP header maps)
might be recycled, because pooled in the first place.

This commit moves the collection and processing of the HTTP trace right
before the response is committed. This removes the need to handle
special cases with exceptions, since by that time all exception handlers
have processed the response and the information that we extract is the
information that's about to be written to the network.

Fixes gh-15819