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Can of expanding foam.

I would go buy a single roll ($15) of fiberglass insulation. If you are looking to add to the soundproofing, you don't want to do all that work and then skimp on that tiny space. Sound travels everywhere and will find and exploit that weakness.

Do it right, you'll be glad you did.

Properly cut the ones you already installed, and you probably have enough for above the door.

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That was my thought when I looked at it

Rockwool is your best bet, but I don't think that glass door is going to be helping with soundproofing.

Please don’t stuff with tshirts or newspaper - fire risk.

Any old pillows?

Most hardware stores should carry a little utility roll of insulation. Usually 16"x48". Significantly cheaper than a bundle of rockwool, but obviously not as good

Dafuq am I looking at? Jesus

Do it right

There’s some special soundproofing insulation out there that you can perches.

Depends on the frequencies you are looking to block. Low frequencies(heavy base, drums) you need high mass. Like a rubber ect.

Mid and low frequencies fiberglass, rock wholl, foam. Ect.

For what it’s worth you can check out the governments STC 50 wall detail found on page 19 (pdf p.33) of ICD 705 liked below.

ICD 705

If you are looking to block lots of low frequencies you need to curb your expect unless you are ready to drop serious $$ as it’s extremely hard to stop but sound cow makes some great products but expensive.

sound cow

Really for any residential application just get as close to the STC 50 wall detail as you can within reason. Note the double layers of drywall.

You could use spray foam and trim it so it is flush.

I would also look at putting something between the studs and drywall to prevent sound from being from the Sheetrock to the studs and resonate on the other side of the wall. A bead of silicone caulk or rubber elastomer.