If it's more or less the same as on my version of Epson Scan 2, you can set a folder to save to at the bottom of the dialog and you need to do this before you start scanning. If that is still set to a folder from a previous scanning session that has since been removed, you could get this behaviour. The dialog you mention to add a page and such is not one I recognise... but I use a bit of a strange scanner so it may be because of that.
If it is an application permission thing, you should have seen a dialog pop up the first time you tried scanning something since your update, asking you whether the app was allowed to access 'Documents' or something like that. To check if that's the problem, go to your settings, Privacy & Security, Files and Folders and see if Epson Scan 2 is allowed to access 'documents'. I am on a newer MacOS version so your settings windows might be slightly different.