Prior to this commit, the metrics `WebFilter` would handle exceptions
flowing through the pipeline and extract tag information right away.
Since error handling turns the exception information into error HTTP
responses later in the chain, the information extracted from the
response earlier is invalid.
In this case, the "status" information could be "200" whereas error
handlers would later set that status to "500".

This commit delays the tags extraction later in the process, right
before the response is comitted. The happy path is not changed, as
handlers signal that the response is fully taken care of at that point.

Fixes gh-11514