What I do left-click (hold) where it says "Link to this set of data" and drag it to my desktop. That makes an icon for whichever browser I'm using on my desktop. I rename the URL icon to something like "FIRECalc 010622" and then file it in a FIRECalc folder. Double-click to open and your saved model is there.
I just started playing with this feature. It's great! Only difference is I right-click and use the "save link as" (or whatever) option and save it directly to my FIRECalc folder. No moving it from the desktop.
I also name things YYYYMMDD, instead of MMDDYYYY. This way they sort in the correct order.