Not a bot :) I'm a member of the community assistance team, we screen messages in this Slack channel as well as in the forum.
I don't currently see a comprehensive way to check how much data has been transferred over the whole instance. As a workaround you could go into each connection and count data per sync. I know this isn't ideal but would get you started!
And to answer the last question, I do not believe Airbyte Cloud includes an initial free sync. This Slack channel and the forum are meant to support the OSS product, so for further Cloud questions I would reach out to sales:
https://airbyte.com/talk-to-sales