feat: publish env to project from cloud editing instance

[AdityaHegde]

Calls PushEnv after creating a connector/source. Also updates the checks for running to also be when deployment is updating.

Checklist:

• Covered by tests
• Ran it and it works as intended
• Reviewed the diff before requesting a review
• Checked for unhandled edge cases
• Linked the issues it closes
• Checked if the docs need to be updated. If so, create a separate Linear DOCS issue
• Intend to cherry-pick into the release branch
• I'm proud of this work!

[ericpgreen2]

Approving, with one question– do we have the necessary error handling in place?

[AdityaHegde]

We show the error like this (forced error, not an acutal error),

While we dont have human readable parsing it should be good for now. This shouldnt happen that often.