Hi @Field ,
I agree with @Pstork1 's thought almost. Currently, within PowerApps, we could not change/assign the property value of another control within current control.
Based on the needs that you mentioned, I think a variable could achieve your needs. I have made a test on my side, please take a try with the following workaround:

Set the OnVisible property of the screen to following:
Set(IsShowButton, false)
Set the OnEnd property of the Video control to following:
Set(IsShowButton, true)
Set the Visible property of the Button control to following:
If(IsShowButton, true, false)
Please take a try with above solution, then check if the issue is solved.
Best regards,