Improve branch manager for a more obvious & faster `mergeability` status

[devversion]

The branch manager has a couple of issues:

• There is a lot queuing going on in the dev-infra repo. This makes the status take longer and cause confusion, causing people to think the status got stuck.
• Improve messaging to avoid confusion. If a PR is pending it may show: Pending — Waiting to check mergeability due to failing status(es), or no status at all until the merge label is added

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