To clarify?...

Hardware-wise, nothing has changed, apart from the new laptop?

UC300ETH's interface to the BoB is unchanged? Power Supplies are unchanged?, Stepper Drivers unchanged?

EStop is connected through BoB input, through UC300ETH then over ethernet to Laptop? That works!

If the ESTOP works then the comms with the UC300ETH is working. I'd be looking carefully at the Mach3 settings, possibly at the port number (rather than pin number) of the axis drives.