All the above are good advice and should be done , but for extra fire protection, I would advise double sheeting the garage side of the partition with 12mm Plasterboard to maintain 1 hour fire integrity. Also any gaps between the framing/house wall should be filled with an intumescent foam/sealant.
Hope that helps,

Rob

I would double tack pink plasterboard if you want to stud the wall. If it was my house I would brick the door way up. It’s more fire resistant than a stud wall will be and the main reason is because you may get cracking. Wood expands and shrinks, your garage will be cold and your house warm. Blocking door ways in like this often leads to cracking even if scrim tape is used to prevent it. It will normally just crack around the edge.

What you have said is perfect that's the way to do it and using kingspan is always the better option as opposed to rock wool. Maybe use an insulated plaster board on the garage side of the stud
help keep the cold out that extra bit.
Regards Ken

That's correct, I would say to infill with a typical stud wall but I would recommend making sure the plaster board used is insulated.