I have integrated PowerApps with a SharePoint list. In PowerApps, the 'Share' option is no longer available, although it was displayed previously. I have highlighted and attached the images for your reference Kindly look at this issue.
You don't need to share the app on an integrated form, the permissions are granted when you are granted permissions to the list. To give another user edit rights, they would only need Design-level SharePoint permissions to the site (you could also have Site Owner).
A standalone app (like the bottom image you provided) will still have sharing options as its permissions are defined by the access list and which role they were granted (user/co-owner)
Cheers,
Sancho
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