As a line manager with a duty of care to your team members you are very well placed to have supportive and helpful conversations with staff about their past experiences – good and bad.
Specifically, with conversations about stressful times, there is strong evidence that positive interactions can assist recovery. It is important to distinguish between clinical and non-clinical interactions. The former should be provided by qualified health professionals who may specialise in helping people who have experienced trauma; while the latter is simply empathetic and respectful ways of engaging and responding to people. This guide applies to the process of talking about stressful times and possible exposure to trauma in the non-clinical sense.
For clarity, you are not expected to diagnose or treat trauma. Your role as a leader is to create compassionate confidential spaces for people to talk to you when they wish to, and to help people seek more specialised help should you both agree it might help. Creating the culture for regular spaces to talk means that people can choose to release stress over time, and when the time is right for them. Expecting people to talk about traumatic experiences in the moment, or when it suits someone else is counter-productive and might make someone feel worse.
It might be helpful to remember that you are responsible to creating compassionate and supportive spaces, and those you lead and manage are responsible for deciding what they want to talk about, when, and to whom.