Is there a minimal working example written in either vhdl or verilog for using the ethernet connection on the cyclone 10 lp development kit?

There's no design example or reference design for Cyclone 10LP devices, but you can try with the following Triple speed Ethernet example for Cyclone III. You may have to modify the design a bit, ie, regenerate the corresponding IP for Cyclone10 LP device, build the HW and SW and test it out. Pay attention to re-targeting the device and the pin outs.

https://www.intel.com/content/www/us/en/programmable/support/support-resources/design-examples/intellectual-property/embedded/nios-ii/exm-tse-sgdma.html