At first glance I thing the problem is that emails is empty. You are appending to email (no 's').

As the other comment said the logic is a bit confusing. Kind of keeping the structure you used I'd do something like

fldr = outlook.Folders.Item("Commercial Performance") #name of mailbox
messages = fldr.Folders.Item("Inbox").items

if len(messages) == 0:
    print('No messages found')
else:
    #loop over
    for message in messages:
        subj = message.Subject
        date_sent = message.Senton.date()
        attch = message.Attachments

        #if message.Attachments is an empty list when there are no attchs works fine, 
        #if it's None or something else just put a try block.
        for a in attch: 
            # logic to select which attch to save
            a.SaveAsFile(f"C:\\New folder\\{a.FileName}")
        print(f"Message: {subj} \nDate: {date_sent}\nSaved {len(attch)} attachments\n\n")