https://en.wikipedia.org/wiki/Transatlantic_tunnel: “The main barriers to constructing such a tunnel are cost first estimated $88–175 billion, now updated to $1 trillion-20 trillion, as well as limits of current materials science.“

China-USA would be a bit longer and go through the ring of fire (https://en.wikipedia.org/wiki/Ring_of_Fire), making it a bigger challenge to build.

I would guess a bare tunnel itself is less of a challenge than its ventilation (even if you build a parallel tunnel tube for ventilation, pumping it out over thousands of kilometers will be challenging. The alternative would be to build ventilation towers every x km) and safety (how long will it take to get an ambulance to a traffic accident? To get people out?)

A semi-bouyant tunnel that sits ~100 meters below the surface with anchors to the floor and floats above might be ideal. Imagine if it was a conveyance even for just "packets" (cargo conatiners that are shot through the tunnel, no humans...)

The next downside is whether anyone would use such a tunnel, given that plane travel would be much quicker, probably safer, maybe cheaper (tolls on such a tunnel plus gas would be quite expensive), and possibly more enjoyable (better views in a plane, it’d probably be depressing and claustrophobic being down under for so long)

I imagine it would be used for shipping primarily.

Simpler to have rail to alaska and cross the Bering Strait by various means I would guess.