When you have multiple e-mail addresses in a single mail account in Mail.app then you need to change signatures manually. Signature plugin helps you in selecting the right signature automatically based on the sender's e-mail address.
Latest supported version is macOS Ventura (13.3) Mail 16.0 (3731.500.231)
To allow bundle plugins in Mail.app type in terminal:
defaults write com.apple.mail EnableBundles -bool true
Download latest build from the Release page
Enabling Signature plugin in Mail.app