Revert "Set default http-based exception as `HttpError`"

This reverts commit 4e1ee661083bd672a884fd13fdb1ffaadea5252a.

This change is a part of a series that is not backwards compatible,
and caused breakage in applications that use the client library.

Change-Id: If614826fb0832602110c1ac8be2c0e6324a5a248
Partial-Bug: #1340596