I am having the same issue.
I can see a list of all my signatures when I create a new mail message, however when I go to Edit Signatures, in the "Signatures and Stationery" form I only see 1 signature and none of the others.
I have tried looking at some of the suggestions in this thread, but none of these have solved this problem for me.
My "E-mail account" list does not have an entry called "Signatures on this device".
The Desktop App suggested to remove is also not present on my system.
I am using the Desktop version of Outlook, Microsoft Outlook for Microsoft 365 MSO (Version 2304 Build 16.0.16327.20200) 64-bit.
Having the same problem occurring on 2 PCs, one using Windows 10 and the other using Windows 11.
Hoping someone can identify what I might be missing here, or provide further suggestions.