Using older versions of Outlook for Mac for personal email and calendar
I switched to 'old' Outlook and my signatures reappeared in the list (along with several blank ones, that I assume were created whenever I clicked the + button in the Signatures panel, but nothing appeared to happen). I deleted the blank ones, set the New Message and Replies signature, then went back to New Outlook and they appeared. (I ahve the Task pane showing, as someone else suggested.) I quit Outlook and restarted it and the signatures still appeared. So we will see what happens.