An apology can ask for relief from guilt before it offers relief from harm.

An apology can be aimed at the wrong relief. Delivered to lift the weight off the person who caused the harm, it puts the injured party in the position of providing comfort, and the transaction gets reversed while sounding entirely correct. You can tell by what it asks for and how quickly it asks.

Before you apologise, work out what you want from it. If what you need is reassurance, get that somewhere else. Then say what you did, without softening or explanation, name the effect on them, say what you will do differently, and stop. Leave the response entirely up to them, including a response that takes months.