There is a subtle but important distinction between readback and hearback.

Readback is when you repeat back the instruction to ATC. You are confirming that you understood. This is your responsibility and is mandatory for certain clearances.

Hearback is when ATC repeats back to another aircraft what an aircraft has read back. This is ATC's verification that the transmission was accurate. For example:

ATC (to D-EFGH): "D-EFGH, CLIMB TO flight level two-five-zero."

You: "Climbing to flight level two-five-zero, D-GH."

ATC (to another aircraft): "...and D-GH is climbing to flight level two-five-zero."

This hearback to other aircraft (or to the radar display system) ensures that ATC has logged the instruction correctly and that other pilots know what has been cleared.

You are not responsible for hearback. That is ATC's function. But understanding that hearback occurs means understanding that ATC is cross-checking all transmissions for accuracy.