webui: Consolidate WebUIManagedInterface specializations

Before this change, we had three specializations of
WebUIManagedInterface. One that supported a receiver and a remote,
one that supported a receiver only, and one that supported a remote
only. This led to a lot of code duplication since we had to implement
almost the same methods across the three specializations.

Bug: 1407936

Change-Id: Ibfa9f81d490b3236e87683fba6a5f01772d514c6
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/4547179
Commit-Queue: Giovanni Ortuno Urquidi <ortuno@chromium.org>
Reviewed-by: Keren Zhu <kerenzhu@chromium.org>
Cr-Commit-Position: refs/heads/main@{#1147632}