This request has been taken up , at least mentioned in the community forum so that Microsoft goes ahead and gives a solution for this .
Something similar to this has been raised and since you are facing a similar problem please vote or leave your comments here .
If your flow is running on an automated trigger then it will always run in the context of an owner of flow (Who created the flow).
So that is who shows up in Modified By field in your SharePoint list.
However the manually triggered flows, like the ones that start with a button in a PowerApp runs in the context of the user who presses the button.
It seems to be possible to change accepted user connections to run a flow in context of the starting user instead of the creators connection.
You should read this article. Maybe this will work for you: https://flow.microsoft.com/en-us/blog/advanced-button-sharing/
Flow runs outside of SharePoint and most likely calls web services, so the only restrictions are normal SharePoint permissions on the user to read or update items. Another way to think about it... any user with read permissions can read data from a SharePoint list using a web browser or the REST API (web services). The SharePoint web services are callable ...
There is no direct way (web part) to add the Microsoft Form in SharePoint Online Classic Pages like there is one in Modern Pages, Use the Microsoft Forms web part.
However, you can add Microsoft Form in Classic page using Script Editor Web Part.
Follow below steps:
Create a Microsoft Form and Click on Share button at top right corner.
Select Embed (</&...