Sorry for the incoming long response, I just want to condense my experience with therapy and try to provide you with something useful.
As others have mentioned, I'd try not to feel guilty about involving them with your problems as first it's their job and second they are doing this as a service for payment, not out of charity; that's not to say no emotion is involved for either party but not being transparent with them is a disservice to the both of you. If you haven't already I'd recommend jotting the most important of thoughts and feelings in a journal or phone notes during the interim between sessions, that way you can steel man yourself so to speak and spend less time trying to articulate yourself in the actual sessions.
I've mentioned this to another user before but I'd recommend asking where the boundary is for 3rd party interference in regards to suicide if you already have broached that topic before. If not then ease into it if you feel comfortable with your therapist.
Through authentic discussion (therapist permitting) you can hopefully distinguish your own priorities about whether you want to pursue the path of recovery or not. Counsellors are trying to help you reach your goals, which in this case I'm assuming is to cultivate a fulfilling / meaningful / content life that has you working towards it rather than closer to catching the bus. Regardless of whether you put in 1% effort or 200% effort, their goal is your goal which for them is outcome dependent not effort dependent. You can really only be the measurer of that effort as tolerances are individual. But even putting in 1% effort if you start identifying as [insert goal adjective, fulfilled for example] (which even for healthy minds, ebbs and flows depending on mood and circumstances) then it's considered job well done.
The inverse of this is putting 200% and the outcomes still remains as not being fulfilled, the list of things to work towards will continue to grow until that changes. Don't shame yourself for not "actively working on yourself" if you are even putting in 1% effort for improvement each day as it's not really a concern for effort but rather result. 1% is good if they are 1% closer to goals YOU want, not others.