should E2E be run in production

Apologies if this is open ended.

Currently my team and I are working on our End to end (E2E) testing strategy and we seem to be unsure whether we should be executing our E2E tests against our staging site or on our production site. We have gathered that there are pros and cons to both.

Pro Staging Tests

• wont be corrupting analytics data on production.
• Can detect failure before hitting production.

Pro Production Tests

• Will be using actual components of the system including database and other configurations and may capture issues with prod configs.

I am sometimes not sure if we are conflating E2E with monitoring services (if such a thing exists). Does someone have an opinion on the matter?

In addition when are E2E tests run? Since every member of the system is being tested there doesn't seem to be an owner of the test suite making it hard to determine when the E2E should be run. We were hoping that we could run E2E in some sort of a pipeline before hitting production. Does that mean I should run these test when either the Front end / backend changes? Or would you rather just run the execution of the E2E on an interval regardless of any change?