Sorry I guess I still do not understand the entire process. But I believe the answer is still the same. Modifying the left navigation bar in Power Automate is not an option. You will have to use another method to send notifications and links to and from SharePoint.
Why can email notification of the approval not be used? You can approve/reject an item via email and send a link to the SharePoint item in the email.( I know the image attached is an over simplification of your problem). Approving/Rejecting does not have to be done within the Power Automate->Action items->Approvals section.
