Yes, the bandwidth depends on the medium through which you are sending the information. For example: standard Cat5e cable will have about 1000mbps bandwidth. For wireless connection, you would need a 802.11ax standard router (5GHz) to achieve the similar bandwidth. POE injector shouldn't have much effect on the bandwidth.
It's best to use wired connection when you can, but if you have a wifi6e router and a wifi6e capable PC network card, then it shouldn't be a problem. Anything less that this and you will have latency issues most likely (depends on what your bandwidth requirements are for a certain script).