Hi Monica,
Not sure this will be helpful or not... I have the same version of macOS and Mail on my iMac as you listed.
Mail serves 4 accounts, only 1 of which had a signature assigned. But when I go to Mail Preferences > Signatures, I see 3 columns:
The leftmost column starts with "All Signatures" and if I click on that I see (in the centre column) Signature #2 and Signature #1
Selecting either of these shows what I have set up for each (in the right hand column.) clicking on the "+"sign below the centre column produced a Signature #3 and in the right hand column I could create a signature there as desired, so all seems to work to this point.
Now moving on to the one account for which I had previously assigned a signature. If I used that account and sent myself an email to one of my other accounts, no signature was attached. But then I noticed the little pulldown under the centre column which says "Choose Signature". The pulldown was set on "None". I then used the pulldown (while that account was selected in the left hand column) and changed the entry from "None" to "Signature #1" Now when I send an email from that account the signature gets entered in the body before I even start typing my own stuff and gets sent properly to the receiving account.
See if your system does this - if not, I haven't a clue how to help.
Dave