Sound typically (*) didn’t require “drivers” or any TSR though. The game had to do all the hardware control itself.
It was usually enough to set a BLASTER variable to point it at the correct IRQ, DMA and memory address, and perhaps run a program at boot to initialize the card and set volume levels, but no TSR eating up memory.
(*) Some exceptions are later soundcards of the Win 9x era that did crappy emulation of a real Soundblaster via a TSR in DOS.
Actually lot less than the browser. Under 300MB, I just checked, and that’s mostly just the network buffer which is 150MB by default.