SecurePixel
I don't use Whatsapp, so maybe someone else can give you better advice later.
But - the way you describe it and looking at your screenshots - Whatsapp seems to want to backup to Google Drive. Since no Google account is selected, it fails. But there is - and that's what you want - apparently the option to make a local backup.
To do this,
a) you may need to enter the correct folder path and
b) depending on where the folder is located, grant Whatsapp access to this folder.
If not known, you can easily grant folder access via the storage scopes: Long press Whatsapp Icon App Info>Storage scopes
or App info> Permissions>Photo and Video (or Files)> Don't allow (+ Storage Scopes)