Playground is being publish from multiple branches, is this the expected behavior?

As background, on Friday I tried to use the TypeSpec Azure Playground and it was down. @chrisradek quickly identified the reason for the downtime:

- *Someone did a release on a backmerge branch - release/november-2024. That apparently runs the publish playground job. However, the November release didn't include all of the core libraries (I only added those last week), so when the backmerge was released, it broke the playground.*

To fix it, Chris ran the pipeline again against main, so the playground got published again in the expected way, and the issue was resolved.

- **Process:** Is the expectation that it gets published on every target branch? Can we move this to only get published from main? Or are there considerations like hotfixes that are involved?
- **Alerting:** Do we have any alert system for when the playgrounds are down? Is this information centralized? Do we get notified, or do we have a dashboard?

Start by inspecting the publish playground job and comparing its behavior on the release/november-2024 backmerge branch and main. Review the pipeline behavior described in the issue, then determine the expected publishing branch and whether existing alerting or centralized status information is available. Done means the publishing policy and outage notification approach are decided and documented or implemented.

Written by the indexing model from the issue text.