Yes, you now have the speed adjust lever correctly assembled. Well done on blowing up that image so successfully, Shifty. You are quite right, the right hand end of the governor spring is shown connected to the loop in the wire link, so that is what you should do. Now as for the spring, Briggs has a number of different ones. Tezza's picture in the other thread shows a longer spring than yours:
https://www.outdoorking-forum.com.au/forum/ubbthreads.php?ubb=showflat&Number=30991#Post30991

Yours may or may not have been modified. The illustrated parts list for your engine shows 6 different governor springs fitted to 60102 engines, depending on the engine's type number. However your type number (0302-01) is not listed as using any of the alternative types and therefore in theory uses the "master" part number spring, which is 260041. I suspect you'd be flat out getting any of the alternative types anyway, so you may be lucky here. I do not know whether the short spring you currently have, is actually an unmodified 260041. If you are sure it has been modified, you need a new one.

Tezza's wire link, in his picture in the other thread, looks as if it is in the second hole from the top of the air vane - but that will be selected to suit the governor spring that he is using. Most likely each of the different springs B&S prescribes for different type numbers of 60102 will attach to a different hole in the air vane. In effect the height of the link-hole above the vane's pivot determines the "gain", or sensitivity, of the governor. When you have the spring you want to use, and you have adjusted the length of the damaged wire link to put the vane in the correct position, you should attach the link to a vane-hole that makes the governor work well: not sluggish (which would mean you had used too low a hole, so the gain was too low), and not prone to "hunting" (which would mean too high a hole, so the gain was too high).