For the average person in SR that cyber replacement was not a option, would have several tools at their disposal.
For the most part, I think a standard commlink with some translation software would be all that is needed for most personal interactions. The deaf person aims the Mic of the commlink at the persons they want to 'hear', the commlink captures their words, and displays them in AR for the deaf individual to read. Done.
Hearing sounds from the environment is an other issue altogether, and the deaf person probably wouldn't be able to pick up on environmental audio clues at all... As the ambient noises would either overload the mic, or even just confuse it with what it is supposed to translate.... After all, <Crashing sound. Breaking glass. Screeching noise.> doesn't really help the deaf person much... Are they approaching an accident? A construction site? A robbery in progress?
And honestly, if the person was born deaf, they would proabably find such info distracting, often relying on their other senses to clue them into the happenings of their environment.