So, here's the weird thing...Systeme actually makes it SUPER easy to share templates with other people...but there's no obvious way to directly turn an email you create into a separate template.
What do I mean? Well, something that shows up down at the bottom when you go to create a campaign step:

So, what I wound up doing was just duplicating the first step and editing it to be my second step, and so on. I also duplicated the campaign when it still had only one step in it, and cleared out the contents of that first step, and named it as a template.
There's a tiny catch, though; you can only have one email campaign in each account or subaccount, if you're on the free plan. So after I created this "template" campaign, I was unable to add any more campaigns, and of course it wouldn't have allowed me to activate both of them at the same time.
Systeme also sent me an email in the wee hours of the following morning to let me know that my account would be restricted in 3 days' time if I did not remove the resources that exceeded the limits of my plan. ๐ Nice of them to give me a warning though, so I went ahead and deleted the extra.
That's fine for now, as I only need one freebie lead magnet campaign at the moment, and when I'm ready to start expanding, it'll only be $17/month or less (depending on whether I pay monthly or annually) to upgrade to the next tier, which has up to 10 campaigns. Super reasonable!
And I have no doubt that once I get the basics set up, I'll be upgrading soon. Systeme is turning out to be very inexpensive and easy to use!