When you manually dial 911 (North American Emergency number), the iPhone does not implement the features in the Emergency SOS feature.
When you make a call with SOS, your iPhone automatically calls the local emergency number… You can also add emergency contacts. After an emergency call ends, your iPhone alerts your emergency contacts with a text message, unless you choose to cancel.
Emphasis Mine
You either have to intentionally activate SOS or have your iPhone/Apple Watch detect a crash or a fall for these features/functions to work.
When your iPhone contacts the emergency number configured in your device, it will send an automated voice message that includes your location. After that call and if configured, it will send text messages to your emergency contacts.
Dialing the local emergency number doesn’t initiate SOS.