Data transmission in ocean
There is no hard limit on depth. This is the same problem as radio communication, except our message is not traveling as waves in the electromagnetic field, but instead as pressure waves.

The Shannon-Hartley theorem relates channel capacity \$C\$, bandwidth \$B\$, signal \$S\$ and noise \$N\$ powers in a channel subject to Gaussian noise. The theorem is:

￼￼$$ C = B \log_2\left(1+\frac{S}{N}\right) $$

This doesn't directly answer the question of "how deep", but realizing that acoustic power, just as electromagnetic power, decreases with the square of distance according to the inverse square law, it's not a big conceptual jump to see that the signal power is a function of the power of the transmitter and the distance between the transmitter and the receiver. If you want to communicate over a greater distance you could:


reduce the noise,
increase the transmitter power, or
reduce the channel capacity.


So to answer your question simply: the maximum depth is limited only by your budget.