No, I saw your other thread and didn't know what that insulation was, so I didn't reply.
You might want to e-mail the picture in your other thread to Owens Corning's "Feedback" people.
Talk to Owens Corning
Owens Corning makes for fiberglass and styrofoam insulation, and I expect someone there might know what that insulation is.
The way to fix that hole would be to use ordinary drywall to replace the missing gyproc lath. When I fix holes in plaster (which is what you have), I'll use 3 inch long drywall or decking screws to fasten short pieces of spruce 2X2 to each side of the hole so they're flush with the existing studs. (You might not have room for those 2X2's if there's a duct or something in that wall cavity.) I use pieces of spruce 2X2 because trying to nail or screw within 3/4 of an inch of the CUT edge of a piece of drywall is invariably going to result in "break outs" (which is where the part of of the gypsum between the screw and the cut edge breaks away from the rest of the gypsum core). Putting up the 2X2's allows a luxurious amount of room to screw the replacement drywall panel in without breakouts.
(There's a bit of skill involved in plastering, and one of them is knowing how thick to mix the base coat plaster so it doesn't slump, but if you're new to plastering, then I'd cheat and use some horizontal wood supports to both apply a uniform thickness of base coat plaster over the drywall, and prevent the plaster from slumping as it dries if you mix it too thin.)
So, if it wuz me, if you widest putty knife is 4 inches wide, I'd use horizontal wooden screeds spaced about every 3 inches. If your base coat plaster is 5/8 inch thick, I'd use about 1/2 inch thick wood screeds made by having any scrap board in the lumber yard's junk barrel cut down to that thickness and then ripped into strips on their table saw. (And, being the perfectionist I am, I wouldn't stick the screeds to the drywall directly with double sided mounting tape. I'd probably stick some strips of painter's masking tape to the drywall first, then use double sided mounting tape to stick the wooden screeds to the strips of painter's masking tape. That would allow me to pry out the wood screeds after the plaster was dry, and pull off the painter's masking tape easily without tearing the surface paper off the underlying drywall.)
Then, paint over the drywall panel with diluted white wood glue and allow time for the glue to dry. Don't paint the wooden screeds cuz you don't want your base coat plaster to stick to them. Try not to let the glue drip behind the wood screeds, too. And, allow time for the glue to dry before applying the plaster.
You can also BUY Base Coat plaster, but the stuff you buy nowadays doesn't have sand in it, and it will often have shreaded news print in it, so it won't end up looking like the real base coat plaster you have now. Normally, base coat plaster is covered by the smoother whiter guaging coat plaster and so you're probably the first one in the history of the World that's wanting to match the appearance of existing base coat plaster. But, if you want to match what you have now as close as possible, you pretty well have to make the same stuff you have, but that not hard to do.
You should know that your base coat plaster will have a working time you can use it for. After a certain length of time, the base coat plaster will go from soft and easy to spread, to stiff and unworkable. I know that's the case for Guaging Plaster (which doesn't contain any sand) but whether or not you'll notice that "kick" as much when most of the material is sand is something I can't remember any more. So, maybe mix up and apply your base coat plaster in small quantities until you learn how long your working time is.
You probably want to run a putty knife around your wood screeds while your base coat plaster is still workable to make it easier to remove them later.
Anyhow, after your base coat plaster sets up, predrill some shallow holes into your wooden supports, drive screws into those holes and pry the wooden screeds out, and then you'll probably need a pair of needle nose pliers to get the masking tape out.
Then paint over the dry base coat plaster (and the screed notches) with more diluted white wood glue, allow to dry and apply another coat of base coat plaster so that it's flush with the surrounding wall. The old plaster will support the new plaster from slumping, and of course, the thinner the coat of plaster, the less it's gonna slump.
Here's the kicker: The thing you're calling "texture" on your old base coat plaster is nothing more than the natural roughness of any dried slurry that's made mostly of sand combined with the impressions made by the stucco brush. (They'd brush the old base plaster so that it was rougher so that the guaging coat would stick better.) If you brush your base coat plaster when it's too wet, then the brush strokes will be more pronounced, and if you brush your base coat plaster when it's too dry, you won't see them at all. You're going to have to experiment as your base coat plaster is drying to see when to brush it to have it look about the same as the surrounding wall.
Anyhow, if your house was built in 1947, it definitely has plaster walls, so maybe it's good you're learning to plaster in your garage as everything you learn from this project will be applicable in your house too. Nowadays, however, no one uses hot lime and sand to make plaster any more both because of the danger in using hot lime and because it's harder to spread smooth and get good results. Nowadays everyone uses drywall for the gyproc lath and a manufactured base coat plaster like Domtar's Perlite Admix Hardwall or USG's Structolite as the base coat plaster. And, of course, drywall joint compound is used as the guaging coat plaster. The only time real plaster will be used is when you're restoring a historic building where it's important to stay true to the materials and methods that were used in the era that it was built.