Overview: If I use a connection in a Canvas App, the signed in user uses their own permissions and the connector as as the signed in user.
Problem: I wish to run a flow as a specific user and not the users calling the flow from the Canvas app.
Hypothesis: I wish to call logging connector into Log Analytics, so I have created a flow, If I use the Power Apps V2 connector, it offers and option to run in another users context.
Resolution: Open the Workflow, ensure you are using the Power Apps V2 trigger, then...
Here I use the Scopes to perform a Try Catch finally set of logic
Tip: most people tend to use a custom connector to push the error message into a function from the Workflow, the function app uses the App Insights SDK and logs the workflow error.
Reza Dorrani has a great recording showing running Power Automate flows using elevated/shared accounts.