Use new context to store outgoing request information

[mydea]

Description

We should store information about an outgoing HTTP request in a new context, e.g. outgoingRequest. This can be used both in browser and node to have additional information about failed fetch/http requests - today, this information is really only visible in breadcrumbs, which is not ideal.

[AbhiPrasad]

I think based on the slack convo we should hold back until we've figured out what the relationship of this context is to https://develop.sentry.dev/sdk/expected-features/#http-client-errors

ref: https://sentry.slack.com/archives/GUCRT2B70/p1743076678224399?thread_ts=1743068974.970659&cid=GUCRT2B70

This should be RFC'd or specced in develop first