Summary:
Prior to this diff, we would only complete or abort a database clone in HandleResponse. However, tasks can fail for other reasons like timeouts. If this happened, the clone would be stuck in the `CLONE_SCHEMA_STARTED` state. This would prevent future clones from the same source namespace.

This diff moves the callback logic for clone into the standard `Finished` function, which is called after any transition to a terminal state.
Jira: DB-15898

Original commit: 9659e6c3ff599a37265d13ec54da753aa0766455 / D43012

Test Plan: `./yb_build.sh release --cxx-test integration-tests_minicluster-snapshot-test --gtest_filter *CloneTimeoutExceeded*`

Reviewers: mhaddad

Reviewed By: mhaddad

Subscribers: ybase

Differential Revision: https://phorge.dev.yugabyte.com/D43085