chore: clean up ConnectionManager.connect

[nirinchev]

Proposed changes

Follow-up on #574 - cleaning up a few bits that seem to have been left behind after several code reorgs.

This is purely moving code around with no functional changes, but simplifies the logic by removing unnecessary variables and branches.

[Copilot]

Pull Request Overview

This is a cleanup PR that simplifies the connection logic in the ConnectionManager by removing unnecessary variables and code branches. The changes maintain the same functionality while making the code more readable and maintainable.

Key changes:

• Removed the unnecessary isOidcConnection boolean variable
• Simplified the conditional logic by directly checking the auth type instead of using an intermediate variable
• Restructured the if-else block to use early return pattern for better readability