It seems you are looking for help on how to approach testing in your organization's multiple environments. In general, it is best practice to run regression tests in all environments where changes have been made, including QA, UAT, and Stage. This is because each environment may have different configurations, data, and dependencies that can impact the behavior of the system.
That being said, it may be possible to minimize the overhead of testing by implementing a risk-based testing approach. This involves identifying and prioritizing the most critical functionality and testing that thoroughly, while possibly reducing the scope of testing for less critical functionality.
One way to do this is to implement smoke or sanity testing in these environments. Smoke testing is a type of testing that verifies that the most important functionality of a system is working correctly. Sanity testing is a type of testing that is used to verify that a small, specific part of a system is working as expected. Both of these approaches can help to reduce the time and effort required for testing, while still providing some level of assurance that the system is functioning correctly.
It's also worth considering whether it is necessary to test everything in every environment. For example, if certain functionality has already been thoroughly tested in QA and UAT and has not changed in Stage, it may be appropriate to skip re-testing it in Stage and focus on testing only the new or modified functionality.
Ultimately, the approach to testing in multiple environments will depend on the specific requirements and constraints of your organization and the risk tolerance for changes. It may be helpful to work with your team to identify the most effective and efficient approach to testing in your multiple environments.