Should SaaS products show a Live/ Production Account Tag?

We've seen projects or apps in accounts on SaaS products showcase a tag/badge/chips to denote that a person might be on a TEST or Sandbox environment. How does this differ when it comes to Live or Production accounts?

Does it help to show that they're on a live account or is it intended that if they're not in the test environment - they're on the live environment.

Here are the test badges for example: