How do I check how far away my AirTag has to be before it sounds an alarm on my iPhone?

Simply leave your Airtag alone and start walking

You’ll get the “airtag” left behind” alert fairly quickly.

It’s not “changable”

AFAIK, moving an AirTag away from your device does not generate any alarm. (although the AirTag will beep occasionally)

If I felt the need to perform such a check (highly unlikely), I would use trial and error - gradually move the AirTag further and further away, let it linger there for a while, and repeat.