Taking everything at face value: You don't like gossip. Your coworkers do and that's pretty much all they talk about.
→ And as a result of that, you decided to stop joining them on breaks.
→ And as a result of that, they did not include you in an informal slack channel, nor did they ask about your personal life. In addition, there is a hostility towards you.
→ And as a result of that, you feel not part of the team in general.
I wanted to summarize your question because I think the cause and effect is clear: You do not share interests so both you and the team disengaged from each other socially.
This is a problem because socializing at work is important to you, but you would like to do it without compromising your ideals.
From a "professional" standpoint
From a workplace perspective, they should not be hostile to you. No angry stares or cold silences. That is unprofessional. I would confront people directly, in a neutral tone with prompts such as: "Is something wrong?", "Why are you speaking to me in that tone? Do we have a problem?", etc. That may not be effective in changing their behavior, but if they are able to provide what I need for doing my job, then that is as far as I will take it. If it is affecting my ability to do the job then I would escalate if I think my manager will help. Ultimately leaving the job entirely if it does not, which I recognize you are already doing.
However, you should make sure are not misinterpreting things. I myself am prone to this at times. Is the silence "cold" or is no one saying anything because there is nothing to say. Is the stare "angry" or does their face just look like that when they are disinterested
Similarly, excluding you from workplace conversations that you need to be a part of for your job is unprofessional. I would address this by directly talking to them and stating as such, escalating as required to get the my job done.
However, if the conversations that are happening are personal / more gossip, you did indicate to them that you were not interested in that sort of chatter so it reasonable for them to not think to invite you to such a channel.
There is a point at which social exclusion in the workplace can become a part of a hostile workplace. It is considered a form of bullying. I cannot make that judgement in this situation without more information. My impression so far is that your workplace is not hostile; you just aren't socially compatible at the moment.
In short: ask yourself if their behavior is directly impacting your ability to do the work you are assigned. That will (hopefully) gain you the support of the company in resolving those issues. After all, they pay you to work and if other people are making you less effective then they are wasting some of their money.
What to do about the non-professional, social aspects of work
Should I continue trying to fit in with them, even though it drains me and might not be sustainable, just for a slightly better environment?
Yes you should try to fit in because you identified a friendly workplace as something that is important to you. No you should not do so in a way that is not sustainable or leaves you feeling compromised.
Should I focus solely on my job and wait for another opportunity?
This is what I would do by default if I didn't want to spend any energy to solve this problem. And, to me, this is what it means to be a professional: get the job done well, get paid, go home. Your co-workers being civil to you is mandatory; being your friend is a nice bonus.
Is there something else I haven't considered?
Yes:
It is possible your coworkers are "venting" not gossiping. Basically they are sharing their completely unfiltered emotions. As in, they have not checked if it is correct or rational before speaking. That filtering takes effort and they are already exhausted by the situation they are in. And it feels good to just say it out loud and have someone listen. It is a way of coping with stress. If someone is venting, you simply listen. You do not have to agree. You can say things like "That sounds awful", "They sound like terrible people". When they are done you can vent about something you don't like in turn, tell a story about something similar happening to you or move on to another topic entirely. You can try and suggest solutions to those problems but it is very likely they don't want to hear it or the problem is already unsolvable and venting itself is the "solution" they've chosen. Now, some people do vent constantly and it is annoying. However, I find most people are self aware and only do it sometimes.
You do not have to be agreeable to be part of the group. You can push back on almost anything. The manner in which you push back is very important. You'll want to acknowledge and empathize with their situation. Express agreement with that parts that you know are correct, point out what you think is wrong and remain open to the possibility that you may be wrong in what you think as well. Do this with a neutral or jovial tone. If you can crack a few jokes along the way that helps. Keep things "light", this is still the workplace, not a dinner party with your friends or a bar. In short: be curious, not very serious and not judgmental. Make no mistake, for a lot of us, this does not come naturally and is a skill that needs to be practiced over and over.
This is a video with two therapists discussing what I mentioned above with more examples and details. You may find it helpful.
Overall, you have a few more options than you think. This situation might be an opportunity to try experimenting with different solutions. It may work or blow up in your face, but since you're leaving anyway...
