I’m already terrible at socializing

Practice. What helped me is to accept the reality of small talk. I used to hate it. I stopped being so invested in conversations. I still try to listen, and ask questions, and be interested, and all that. But it's OK to talk about the weather or mundane stuff like that, keep things light, walk away when it's natural, and forget about things. Not be so invested.

Appreciate and integrate the difference between small talk and deep philosophical conversation. They are both important and both have their place. Small talk comes naturally to extroverts. Introverts (me) have to work a little harder at it.

it’s especially difficult for me to create genuine friendships with women because I can’t help thinking of them as “possible future partners” (or some bullshit like that)

Folks may not like this, but if they're "possible future partners" then they're not genuine friendships. They're dating prospects. It's fine to be interested in dating women, but as soon as you have an inkling of interest, ask them out on a date. Say the word date. If they say no, respect that, and accept that they are not available as potential future partners. You want your choices to be respected. Respect the choices of others. Asking people out is hard. I know. So is being rejected. I know. That's life.

I would like to feel more comfortable with my singleness

Once you achieve that comfort, you will become more attractive. I think this is another matter of practice. Go do fun things by yourself! Things that you want to do! Eat out, go to the movies, travel. Not so much to meet other people but because you find fulfillment in those activities for their own sake.

while forging more non-romantic relationships with other people.

Make small talk with folks you are not attracted to. This takes a bit of the edge off and it helps with the practice. Their insight and opinions are just as valuable as those of the folks you're attracted to.