It appears what causes it not to run is bug in Power Automate -- or just bad semantics, which is more in-line with MS product design.
The PA command for Teams called "When a new channel message is added" does not initiate an action for any message, it only initiates when a new *conversation* is added, and not when replies to a conversation are added. The name of the command is ambiguous and confusing. This theme in MS products is why I'm trying to get the information outside the MS ecosystem as soon as possible so I can script the automation like a pro.