TL ; DR - Yes, ANY form of summon requires either Enhanced autopilot (not available to purchase any longer in the US) or FSD.
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Perhaps this webpage from tesla can show you the feature set that comes with "autopilot" which your car has, vs "full self driving" which is the 10k additional purchase (or $199 per month subscription)
Autopilot is an advanced driver assistance system that enhances safety and convenience behind the wheel. When used properly, Autopilot reduces your overall workload as a driver. Learn more about Autopilot.
www.tesla.com
The relevant part of the web page is posted below:
View attachment 716510
You can clearly see that the only thing that "Autopilot" includes is traffic aware cruise control and autosteer. Both "summon" and smart summon are part of FSD.