I'm currently on a break with my partner and I'm unsure of how to act.

I experienced a significant burnout that left me feeling overwhelmed by anxiety and depression. The turning point came when my partner expressed how harshly I had been treating them and mentioned wanting to take a break. That conversation happened nine days ago. I returned to my home country to focus on managing my anxiety and depression, and now we're navigating a long-distance relationship. My partner is also struggling with depression, which has worsened since the break. They feel guilty for initiating it and are hesitant to express love or even allow me to refer to myself as their boyfriend, which I believe stems from their feelings of guilt. Despite this, my feelings for them remain strong. I want to show them how much I care and win them back, perhaps by doing some romantic gestures or being more affectionate. I worry that if I keep our interactions too casual, I might lose them completely. I'm uncertain about the best way to handle this break, but I genuinely love them and believe I can mend the hurt I caused. I truly see a future together. What steps should I take to address this situation?