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Dear Errrrrrrrrrik,
Thank you for the reply.
If you don't want to manually copy the fields, it is possible that Microsoft Power Automate could meet your requirement to export the Form responses to Excel file saved in SharePoint automatically.
I found a thread which has the similar query with you in Microsoft Power Automate Community, such as: Solved: Form Response to Excel Spreadsheet - Power Platform Community (microsoft.com). So my suggestion is to post on dedicated Microsoft Power Automate Community, and you will get a more detailed and professional answer to your query there.
We appreciate your understanding.
Sincerely,
Jazlyn | Microsoft Community Moderator