Hi @LaurentF,
How do you submit your form data (in Screen1, Screen2 and Screen3) within your app? Using Patch function?
I agree with @tchin-nin's thought almost. You could create three separated screens based on the following blog:
https://powerapps.microsoft.com/en-us/blog/separate-custom-forms/
I have made a test on my side, please take a try with the following workaround:


Note: FormScreen2 and FormScreen3 are both duplicated screens from the FormScreen1 (just as mentioned within above blog I provided).
Set the OnNew property of the SharePointIntegration control to following formula:
NewForm(SharePointForm1);
Set(StepValue,1)
Set the OnEdit property of the SharePointIntegration control to following formula:
Set(StepValue,Value(SharePointIntegration.Selected.Step)+1); /* <-- Step represents the Step Column in your SP list */
If(
StepValue=2,
Navigate(FormScreen2,ScreenTransition.Cover);EditForm(SharePointForm2),
StepValue=3,
Navigate(FormScreen3,ScreenTransition.Cover);EditForm(SharePointForm3)
)
Set the OnSave property of the SharePointIntegration control to following formula:
If(
StepValue=1, SubmitForm(SharePointForm1),
StepValue=2, SubmitForm(SharePointForm2),
StepValue=3, SubmitForm(SharePointForm3)
)
Set the Default property of the TextInput control within the Step Data card in each Edit forms (SharePointForm1, SharePointForm2 and SharePointForm3) to following:
StepValue

Note: Actually, the SPintegration @tchin-nin mentioned is the SharePointIntegration control.
The GIF screenshot as below:
More details about understanding SharePoint forms integration, please check the following article:
https://docs.microsoft.com/en-us/powerapps/maker/canvas-apps/sharepoint-form-integration
More detailsa about customizing SP list custom form, please check the following article:
https://docs.microsoft.com/en-us/powerapps/maker/canvas-apps/customize-list-form
Best regards,
Kris