I think it is worth discussing what "empathetic" means to both of you, as I get the impression that you have differing perspectives. For example, I noticed you said that you listen to her problems and try to find solutions. Some folks find that "problem-solving" behaviour invalidating rather than empathetic, while others actually prefer that approach. It is hard to know which camp your girlfriend falls into without having a frank discussion. I would also consider what behaviours or attitudes she would need to display for it to come across as empathetic to you. Maybe she also feels like she's appropriately listening, even though that's not been your experience. It is hard to pin these things down and have these discussions, but if you can manage it, it will greatly enhance your communication with each other.
Also: don't let it being a tough time become a reason to shelve your feelings. I say this as someone who did that for four years because my partner was always going through some hard time or another. All that bottling up has almost ruined my relationship, so don't be me. But do be tactful and sensitive. Ask her what she needs from you in this tough time, be willing to give what you can, and let her know you feel like you two have some communication issues and you want to be really clear on what's working well and what isn't in your relationship. Give her space to share her feelings, share your own, and then try your best to figure out how to approach the problems as a team.
If therapy is accessible to you and you can find a competent therapist who has a good approach for you, then consider making an appointment. It can be good to talk to a third party about your burnout and feelings of depression (which is what this low motivation sounds like to me). Your gf may not be able to give you the emotional nurturing and assurance that it sounds like you're seeking right now, but you can find tools and help elsewhere too.
Good luck!!