External Monitor Blurry text and Sluggy Mouse on MBP 2020
How is your HDMI cable connected to your USB-C on the MBP side?
I had similar issues and realised that certain combinations of HDMI or HP Display port cables in conjunction with cheap Ali-express converters to USB-C resulted in either a blurred external monitor or even sometimes in the MBP monitor being blurred and the external monitor being perfectly clear.
So if you have the chance, try using different cable combos, just to see if it makes a difference.