You can get “sprinting shoes” (light XC/track flats) for like $20 (old versions) on ebay/amazon etc. Just search “cross country flats”, or “xc flats”.
These are crazy fast shoes, I have a pair but they are a half size too big. Even then, they make you feel so springy, definitely great for forefoot dominant sprinting/running etc: $20
Tons of results. XC flats are great for sprints/short intervals. They are also great on grass, any distance. If you find something, just try and find the official shoe specs and see if it’s < 5 oz. A good shoe for sprinting should be about <= 5 oz. Generally the lighter the better. You probably won’t find anything under 3. So, 3-5 oz is a solid range for shoes to sprint in.
Once you realize how cheap XC flats are, you shouldn’t worry about shoe cost etc. The shoes I mentioned first are < 4 oz, crazy strong/durable, and engineered to make you fly. Definitely more intense on the lower leg because of what they are built for, but that’s expected with sprinting.