Hi @Anonymous ,
Could you please share a bit more about your scenario?
Do you want your custom Dropdown component to display the selected option/value when you edit an submitted record in your Edit form?
I have made a test on my side, and don't have the issue that you mentioned. Please take a try with the following workaround:

Set the OnVisible property of the Edit screen to following:
UpdateContext({showList: false})
Set the Default property of the ListBox to following:
If(!IsBlank(ThisItem.Status.Value), ThisItem.Status.Value, "")
On your side, you should type:
If(!IsBlank(ThisItem.YourChoiceColumn.Value), ThisItem.YourChoiceColumn.Value, "")
Set the Text property of the DataCardValueN label to following:
If(!IsBlank(ListBox1.Selected.Value),ListBox1.Selected.Value, "")
Please check the following GIF screenshot for more details:
I have also provided a sample app, please check the following attached Sample app.
Please check if you have bind the ListBox within your Edit form to the Choice column in your SP list property. And have typed above proper formula within the Default property of the ListBox and the Text property of the DataCardValueN label.
Best regards,