I feel for you so much as you navigate your way through depression on top of developing a relationship that holds within it not just 1 sensitive (person) but 2.
Please don't be too hard on yourself for feeling the need to vent. Feeling the need and giving yourself the freedom to fulfill that need is important, for mental and physical wellbeing.
Wondering if your partner has ever felt the deep need to hug anyone. This doesn't necessarily mean he won't one day feel it. Maybe he'll only feel it when he feels deep sorrow or incredible joy (an extreme situation). When you're depressed, is there anything he does feel the need to do, in the way of comforting/supporting you? For example, maybe he feels a deep need to put on certain music to distract you from your thoughts or maybe he feels the deep need to lead you to question your thoughts (make sense of them).
A strange suggestion but do you think he'd be able to brush your hair when you're feeling upset? Is this something he could manage, based on his sensitivity to touch? Do you feel this would somewhat calm you and lead you to feel more loved through a challenge? Does he hold the ability to lead you to feel deep connections through something other than hugging? Can you imagine somewhere down the track you both find a middle ground? By the way, hair brushing is known to release and promote certain chemistry in the brain. I discovered this one day when I wondered why people experience that 'zoned out' relaxed look on their face. I couldn't help but wonder why this happens. Who would have thought - hair brushing triggers a chemical reaction. We're quirky creatures, that's for sure.
If you're super sensitive to a lot and sensitivity is natural, does this make you super natural? If you're super sensitive to feeling your thoughts, to sensing how others are feeling, to sensing what's needed in a situation, to sensing the need to question and wonder, to sensing what brings you down and what raises you and so on, you have an incredible ability, which can feel like more of a curse at times.
Have you ever wondered about the incredible abilities of someone on the autism spectrum? There can be a stack of them. The ability to emotionally detach, while in search of reason can be one (objective analysis). Of course, this does present issues at times. If your partner possesses this ability, objective analysis, he may resemble a live in psychologist to some degree. Is it possible you are both 2 halves of a whole?