Can transmission make car sound rougher?
 

300D 82.
Car was driven with low transmission fluid.

transmission may well be buggered then...

drain transmission, inspect oil, drop access panel and remove filter and inspect.

would a buggered transmission make the car sound rougher

Rough as in grindy noises or idle/acceleration rough?

It's as if the car sounded smoother and quieter (turbo diesel) and now it's as if the engine sounds louder and rougher (like a non turbo)

Gears shift just like before i.e. there seems to be no problem with the transmission itself but it's as if the engine sounds louder.

I see no reason for tranny fluid loss to affect the noise of the engine in any way.
did you perhaps drive at 5000rpm for extended periods due to this loss of fluid? did you mistakenly pour the transmission fluid into the gas tank by mistake?
more likely, your fuel filters are dirty, and the car is running rough because of air, or you are paying extreme attention to the car because of the fluid loss, and you are only now noticing the noise.
by any chance are you now driving with the windows down?

Engine or transmission mounts are my first guess, if sagging or improperly installed (tightened in non-settled position), next would be the possibility of the exhaust touching one of the hard-rubber bumpers under the car.

Idle it in drive, then idle it in reverse, see if there is any difference in "roughness" or engine sound transmitted into the chassis. If quieter in reverse, right engine mount, if in drive, left engine mount, either could indicate exhaust rubbing.

Just a hunch based on my 60x / 124 experience, might not transfer to your model.

fuel and air filters all changed and I thought the noise increased very slightly after that.

car was driven on freeway several times with low fluid.
what happens to transmission when fluid is low?

no fluid poured into gas tank

not driving with windows down.

How low are we talking here. Obviously not so low that it could still operate. If it was still on the dipstick most likely no harm was done.