That's it. Perfect.
That code says it is what Apple called "AirPort Extreme 802.11ac." It was introduced in 2013 and discontinued in 2018, and was the last AE model in the series.
These are Apple's tech specs showing supported protocols and security measures,
AirPort Extreme 802.11ac - Technical Specifications - Apple Support
I believe all Airports can be used in repeater/extender mode. It should be fast enough to give performance well today. If WAP2 is not secure enough, then you will need something else.
The Airport Utility App— which should let you set up repeater/extender mode—is still a part of the latest macOS, so you should be able to manage it without issue. Not sure how it is managed from Windows, but specs say it is compatible.
EDIT: Ah! Apple has a Windows version of Airport Utility: AirPort Utility 5.4.2 for Windows - Apple Support
Will try to respond as best I can to the other questions (our old 1Gen Airpot died several years ago so I'm a bit rusty):
— If I unplug it from my regular home router, will it still work?
If healthy, it should be fully independent and free-standing. However, you may need to set it up again for a new location. We never traveled with our old Airport.
— Do I need it plugged in?
Yes. It is not battery-powered.
— And if the security is bad, how can I improve it?
Apple have released firmware updates along the way. Airport Utility should let you check for updates. The last updates I see in searching Apple support were in late 2023.
— If I get told that its more secure than regular public restaurant wifi, then is it ok right?
WPA2 is still a widely-used security measure and, with Airport Utility, you have full control over assigning passwords. Businesses tend to have easily-entered and blatantly obvious passwords, like "Mama_Marys_Southern_Cafe." You can do better than that.
That all I have. Post back if needed.
Allan