How does an implant send out the data of a thousand electrodes through the skin? · Grey Matter

It does not send the raw signal.

How does an implant send out the data of a thousand electrodes through the skin?

It does not send the raw signal. Sampled at 30 kHz with 10 bits, a thousand electrodes would produce about 300 megabits per second, far more than a low-power radio link through the skin carries on the power an implant can spend. Chips like those in the N1 amplify, digitise and detect spikes on the implant, then send only the times of spikes or compressed features per channel, which shrinks the stream by orders of magnitude and still carries what decoders of movement use.