Hi @Anonymous ,
Based on the needs that you mentioned, I afraid that the Gallery control could not achieve your needs directly. As an alternative solution, I think the Data Table control could achieve your needs.
If you want to add a Button control within the Data Table control, I afraid that there is no way to achieve your needs in PowerApps currently. As an alter native solution, you could add another column within your Data Table to act as a Button click option.
I have made a test on my side, please take a try with the following workaround:

Add a Data Table control within your app, set the Items property to following:
AddColumns('YourSPList', "Action Operation", "Button Click")
then enable the "Action Operation" column in your Data Table control.
Select the "Action Operation" column in your Data Table control, then set the IsHyperlink property to true, then set the OnSelect property to following formula:
"Type your Button Clickable formula here"
Please take a try with above solution, then check if the issue is solved.
Best regards,