The problem you have is your flow is running in the context of you. As it’s running as you, you don’t have permission on the end users calendar to create an event.

I have been able to add events to users calendars but done it within the power app as that’s ran in the user context, but I didn’t need to have an approval step, so I had the user book a session in the app, it add the session to their calendar, then write that data to SharePoint. My flow then just scanned for new items created in SharePoint to send them a confirmation email.

I’ll have a play with having the power app handoff to flow, let flow handle the approval then see what the flow can hand back to the power app. Not sure it will work but worth a try