Actually this seems not like a good aproach to rely on another plugin, so that yours will not break something. Also I have not even configured S3 in backup and still the aws sdk is loaded somehow.
On a side note since we updated our wordpress to 5.4.2 the plugin is not shown anymore in the menu. I’m not sure if it also has to do with the aws sdk issue. But disabling w3tc doesn’t bring back the menu entry of backwpup. Backup jobs seem to be running, because they are triggered by cronjobs.
I’m very disappointed of the plugin in its current state.