Hi @PowerAid,
Do you want the RequestStatusVar value not to be passed to another record, and not to be lost in previous record?
I agree with @Srautio's thought almost, the Context variable (created via UpdateContext function) is scoped to a screen, which means that you can't build a formula that refers to a context variable on another screen. If you don't close your app or change its value, it would remain its previous value continuously.
I have made a test on my side, please take a try with the following workaround:

Set the OnVisible property of your Edit screen (on your side, it is Edit view) to following formula:
UpdateContext({RequestStatusVar:Blank()}) /* Initialize the RequestStatusVar variable when you create a new form */
Set the OnSelect property of the "Update" button to following formula:
UpdateContext({RequestStatusVar: "New"}) /* Update the RequestStatusVar variable when you click the button */
Set the Default property of the TextInput control within the Request Status Data card to following:
If(
EditForm1.Mode=FormMode.New,
RequestStatusVar,
Parent.Default
)
Or
Set the Default property of the Request Status Data card to following:
If(
EditForm1.Mode=FormMode.New,
RequestStatusVar,
ThisItem.Request_x0020_Status
)
The GIF screenshot as below:
Best regards,
Kris