T7878: Using mergify rule to handle conflict checks for private repo

[kumvijaya]

Change summary

Using a Mergify rule to handle conflict checks for a private repository.
Observed that Mergify detects conflicts more accurately and is more reliable compared to a custom action.

Note:
It is only for private repo., public repo will continue to use github workflow.

Types of changes

• Bug fix (non-breaking change which fixes an issue)
• New feature (non-breaking change which adds functionality)
• Code style update (formatting, renaming)
• Refactoring (no functional changes)
• Migration from an old Vyatta component to vyos-1x, please link to related PR inside obsoleted component
• Other (please describe):

Related Task(s)

https://vyos.dev/T7878

Related PR(s)

Checklist:

• I have read the CONTRIBUTING document
• I have linked this PR to one or more Phabricator Task(s)
• My commit headlines contain a valid Task id
• My change requires a change to the documentation
• I have updated the documentation accordingly

[github-actions]

👍
No issues in PR Title / Commit Title

[dmbaturin]

I have no objections against the change.

Just a note: please do not use https://vyos.dev/T6707 as a parent for these tasks. This isn't even related to the release workflow at all. Those tasks should also have better (at the very least, non-empty) descriptions to make it clear what exactly is being done and why.