You would be able to create a customised approval flow using Azure Logic Apps (https://learn.microsoft.com/en-us/azure/logic-apps/quickstart-create-first-logic-app-workflow) which allows you to choose different methods of notification. You may need to create a script or two to achieve exactly what you want (particularly in regards to granting permissions to resources) but nothing too complicated.
Update
I found the following page which may further assist in achieving what you need.
You would be able to create a customised approval flow using Azure Logic Apps (https://learn.microsoft.com/en-us/azure/logic-apps/quickstart-create-first-logic-app-workflow) which allows you to choose different methods of notification. You may need to create a script or two to achieve exactly what you want (particularly in regards to granting permissions to resources) but nothing too complicated.
Update
I found the following page which may further assist in achieving what you need.
https://gotoguy.blog/2018/09/15/create-your-own-azure-ad-pim-app-with-powerapps-and-flow-using-microsoft-graph/
It is possible to connect PowerApps with Azure Logic Apps with the connectors available.