Use 5/8" sheetrock, it blocks like twice the sound of 1/2" for almost no additional cost.
That just isn’t true, sorry.
An STC (sound transmission) rating for a ’standard’ wall with 1/2" drywall on both sides is about a 33 STC rating, an insulated wall with *two layers* of 1/2" drywall *on both sides* is about 44, a wall with 5/8" on one side and *two* 5/8" layers on the opposite is about 55. We still have not achieved ’twice’ the stc rating, and we are well beyond what an existing 1/2" on the existing interior wall, and a new 5/8" layer on the garage would achieve, but it wouldn’t be as effective as two layers of 1/2" on both sides, an increase of only 11 STC points.
Can you achieve twice a standard 2x4 with 1/2" drywall 33 STC rating? Yep, you can get to 50-60, but not with a single layer of 5/8". Would it help? Yep, but not in reducing the transmission by 1/2.