hydrostatic transaxle faster

I mostly hear bad things about hydrostatic transmissions like how you can't pulley swap them and stuff. So I was wondering if there is anyway to make a hydrostatic transaxle have a bit more speed

From my experience, hydroatatic transaxles are not actually "bad" per se, and most people that say they are just junk are misinformed.

They do however comsume more engine power than a geared transaxle and as you said they don't allow for any increase in input speed. Pretty much all you can do is but some bigger tires on the rear to get a slight speed gain.

In my opinion it's not really worth trying to get too much speed from a hydrostatic tractor anyways due to the engine braking you will get when you push the clutch in at high speeds. Instead of rolling to a stop like a geared transaxle would allow, it would jerk to a stop instantly. Not really ideal.

it can be pulley swapped on the engine side, that's not saying it's going to do much good, over driving a hydro will most likely destroy it in a short amount of time, in my experience there's only 2 ways to get more speed out of a hydro and make it last, one is bigger tires, not much speed to be gained here but you can get a few mph more depending on the tires size, the other is to relocate the hydro and run a chain drive off the axle shafts to a solid axle that is positioned in the original location, red neck computer geek did a video showing this very thing, from there you can play with the sprockets and gain speed, I personally like a hydro for trail use and light mudding, in my opinion they offer superior control in trails where you have steep hills and rough terrain and would be generally riding at a slower pace

I have mildly pulley swapped a hydro to get more speed successfully.  In shorts trips it was okay but after running it for an hour the hydro unit would overheat and spew fluid out of the vent.  So I went back to my original engine pulley.  Good for slow speed working but not great for speed.