I've had episodes of depression throughout my life and I have found yoga to be hugely beneficial to my mental health. Obviously it's not enough if you have severe or even moderate depression, but it has helped to relieve mild depression for me.
I have also tried CBT, counselling, mindfulness, and antidepressants. I think they can all be helpful (individually or in combinations) depending on the person, the severity of the depression and the reasons for it.
OP, did the GP take you through a diagnostic questionnaire for depression/anxiety and tell you your scores? Do you have a sense about whether your depression is mild or severe?
Based on what you've said about your feelings and your relationship, I think counselling could be very beneficial.
As for the sertraline, it's a tricky decision IMO. You certainly haven't "failed" if you take them. I was prescribed it once before and decided not to as I was anxious about side effects and wanted to manage without. But recently I did start taking sertraline - I felt my depression was worsening and with many of my usual strategies unavailable due to lockdown, I decided to go for it. The side effects were unpleasant to begin with, they did subside but it would have been difficult to get through the initial stage without telling my husband.
So if you do take sertraline I think ideally you would tell your husband, but it sounds as if there could be lots of issues in the relationship (which are probably contributing to your depression) so if you don't feel able to, that's fair enough.
Good luck whatever you decide.