AT&T does support WiFi Calling - https://www.att.com/features/wifi-calling/
So you just need WiFi
Your queries:
you mention using WiFi Calling across Starlink at major events.
Answer: I run a company which provides WiFi to events, we use both individual starlink kits and starlink kits plugged into " Mesh " Wireless - Where we can push internet to say 15-20 different areas across a large music festival.
Are these major events at locations away from the location of your own Starlink system?
No, you've ventured down a rabbit hole - WiFi Calling/WiFi doesn't just connect to all starlinks, ONLY the WiFi networks that you're connected to.
Could you explain exactly how your cellphone would access a Starlink system other than your own?
As mentioned above you're assuming that I can roam on WiFi Calling and use everyone elses WiFi - Not the case. You can only use WiFI networks, where you have the password and your connected. - WiFi is not intended to replace cell signal... its lower range.
I assume that your phone would be detecting that Starlink system's router's wi-fi; would it not usually be password-protected to prevent it from being overwhelmed by many users?
See above.
WiFi Calling runs on top of WiFi, it uses the internet - It will work across any WiFi with at least 2mbps/2mbps up and down.