I am unable to append rows to a Google Sheet when I upload an Excel (.xlsx) file. What are the conditions to make it work?
If you upload/drag-n-drop an XLSX file to Google Drive, you should be able to edit that Sheet immediately provided you convert it to Google Sheets format. I don't believe that if you preserve the Microsoft format, that you can edit an XLSX file saved to Drive.
From your screenshot, it looks like you're in the Sheets app and importing an XLSX -- if that radiobutton stays at "create new spreadsheet," it will create a brand new Sheets file in your Google Drive for which you should be able to edit immediately.
I just tried both techniques (both single & multiple sheet spreadsheets), and both are WaI (working-as-intended). If you provide an error, or screenshot of an error while appending rows and its failure, then perhaps we can help out more.