In T124080#1948655, after a SWAT deploy, a GLAM contributor noticed the change weren't propagated on Commons Beta even when propagated on the main cluster.
@hoo has indicated to me there is an automatic process to sync configuration, later on.
A documentation would be interesting to explain this sync and when it operates.
It is mostly Jenkins driven via a job that runs every 10 or so minutes. There is some overview at https://wikitech.wikimedia.org/wiki/Nova_Resource:Deployment-prep/How_code_is_updated albeit it hasn't been proofread in a while...
For the root cause, I noticed the Jenkins jobs running on beta cluster are deadlocked. Which is hitting us from time to time :( Fixing it.
I tidied and updated that page a little, it sounds like we already have this documentation and the issue with the process that existed at the time of ticket creation was resolved shortly afterwards by @hashar.