[Github] Update Logs Private Repository Sync Errors

[parth-elastic]

Related to https://github.com/elastic/connectors-py/issues/2636

Included rate limit related information in debug logs

Checklists

Pre-Review Checklist

• [x] this PR does NOT contain credentials of any kind, such as API keys or username/passwords (double check config.yml.example)
• [x] this PR has a meaningful title
• [x] this PR links to all relevant github issues that it fixes or partially addresses
• [x] if there is no GH issue, please create it. Each PR should have a link to an issue
• [x] this PR has a thorough description
• [x] Covered the changes with automated tests
• [x] Tested the changes locally
• [x] Added a label for each target release version (example: v7.13.2, v7.14.0, v8.0.0)
• [ ] Considered corresponding documentation changes
• [ ] Contributed any configuration settings changes to the configuration reference
• [ ] if you added or changed Rich Configurable Fields for a Native Connector, you made a corresponding PR in Kibana

Changes Requiring Extra Attention

• [ ] Security-related changes (encryption, TLS, SSRF, etc)
• [ ] New external service dependencies added.

Related Pull Requests

Release Note

[parth-elastic]

@parth-elastic do you think these logs will be sufficient to investigate the problem?

Yes, we tried to cover all the pieces of information required to debug this issue. Since the issue was regarding the rate limit, we've already covered the exceptions and logs related to that.