[Code Health] Remove uses of base::SupportsWeakPtr

(/services/network)

This CL removes uses of this deprecated base class by adding a
base::WeakPtrFactory data member.

In some cases, the base class was no longer being used, so it's
simply removed.

This CL was uploaded by git cl split.

R=cduvall@chromium.org

Bug: 647430
Change-Id: I975034d850efc035cbdb3bd0b1247a7fcf02b40e
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/5515943
Auto-Submit: David Bertoni <dbertoni@chromium.org>
Commit-Queue: Clark DuVall <cduvall@chromium.org>
Reviewed-by: Clark DuVall <cduvall@chromium.org>
Cr-Commit-Position: refs/heads/main@{#1296379}