Stop dropping requests in DigitalAssetLinksHandler

This class was only capable of handling one request at a time, which
made it very problematic to use as an instance variable.
If it was called multiple times, it would drop ongoing network
requests and never respond.

This CL solves this by tying the lifetime of the url_loader directly to
the request itself instead of having a single instance tied to the
lifetime of the Handler. It also passes the client code callback through
the internal callbacks instead of saving it as an instance variable.

The traffic annotation is updated with new required fields, and to
reflect that cookies are not being sent or stored as part of this
request.

Fixed: 361370185
Change-Id: Id9a85496a79f8a1cc85cce1d70b656809fe77f25
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/5832529
Reviewed-by: Peter Beverloo <peter@chromium.org>
Auto-Submit: Peter Pakkenberg <pbirk@chromium.org>
Reviewed-by: Chris Mullins <crmullins@chromium.org>
Commit-Queue: Benoit Lize <lizeb@chromium.org>
Reviewed-by: Benoit Lize <lizeb@chromium.org>
Cr-Commit-Position: refs/heads/main@{#1352811}