My recommendation (not a doctor) is to makes it easy for them to engage, so it is almost accidental.

With burnout, at least in part, and depending on the person, there is a tendency to withdraw. Invite them to go do something already planned, that they don't have to pay for, that won't take too long and you know they enjoy. Then just be a friend without expectations.

I think advice and suggestions can make things worse because making a decision or taking action is often the thing that has them locked-up.