I (24M) feel exhausted of trying to keep together my relationship with my (25F) gf of 5 months

This is a very complicated story so I’ll try to keep it simple. I met my (now) girlfriend in January after she broke up with her boyfriend of 3 years because she said she was bored. He kicked her out when he found out she was meeting with me (we worked together), and we ended up moving in together right away because she had nowhere else to go. At work we were great friends, joking around all the time, but we knew deep down we couldn’t be together because our values are completely different — I believe in inclusivity, human rights, being yourself, etc., while she is more conservative and doesn’t agree with a lot of those things.

Still, the sex was great, and we became FWB. Then in March, I got my dream job in a city I’d always wanted to live in, about 1.5 hours away. She wasn’t happy but accepted it. I started working hybrid — 3 days remote from our apartment and 2 days in the office in the new city. That’s when she wanted to make things “official,” and I went with it, telling myself I “live in the moment.”

By May, we were talking about moving in together in my new city. But because of her job and studies in the old city, she said she needed more time — maybe until the end of the year. I didn’t want to lose the opportunity of my dream city, so we agreed on a semi-long-distance relationship.

Since then, I’ve realized how different we are. She’s a very cold person emotionally, and communication is basically nonexistent. I love talking through problems after cooling off, but she refuses and even told me that in her last relationship they “barely talked about anything” and that was “fine” for her. Because of this, I’ve developed a habit of staying silent instead of trying to resolve issues — which is killing me inside.

Now it’s August, and I only see her once a week. I keep finding myself thinking she’s not the one for me:

• Our values don’t align.
• When we argue, she refuses to talk. Not always, most of the time tho, and I really need to talk deep to make her talk.
• She believes the man should always pay for everything — and gets mad when I want to split bills, which is harder now because living alone is more expensive.
• She’s does not seem really interested in my hobbies, even though she says she is. She never asks questions or engages much, just says “that’s nice.”
• She asks me about my day every day, but when I share details, she never digs deeper or keeps the conversation going.
• Her only hobby is playing World of Warcraft. I am genuinely interested in her adventures but this is her only hobby, and it just doesn’t appeal to me.
• I’m tired of being the only one putting in effort. I’m always the one to initiate dates, check in about her day, and keep the connection alive.
• When I upset her, she gives me the silent treatment, which I despise.
• OFC, I’m not a saint, I’m young and I sometimes shout when I’m very angry at her (which I am trying to work on), I sometimes don’t understand her ADHD problems, and I know that she’s trying her best, because she started therapy and maybe with time things will get better.
• She does have confirmed ADHD which explaines a lot of her behavior.
  Now she’s on vacation with her family, and she’s stopped sending me good morning/goodnight texts. When I mentioned it, she just said, “I’m on vacation,” which made me feel confused because to me, couples do small things like that when they care.

Before this relationship, I had really good self-esteem and had been doing well in therapy. Now, I’m questioning myself constantly, wondering if I’m just “too needy” or if something is wrong with me. She hasn’t cheated, and sometimes she sends me sweet messages or calls me her “cutie pie,” but then other times she’s so distant that I feel completely alone.

I love her, but I’m starting to think we’re just incompatible, and I’m exhausted from carrying this relationship. Part of me wants to break up, but another part is scared — scared that the dating world sucks now, and maybe scared that I am loosing something real here, my parents said that they were very simmilar to us, and with just enough effort they made it through, and now they love each other more than ever before.

How Is this situation fixable? How, if she doesnt want to talk about fixing it? Is there some kind of word combination that I don’t see? Or maybe Im gaslighting myself into that situation and everything is fine as it should, and I just only have too big standards?

TLDR; Started as FWB with a coworker, became a couple when I moved to a new city. Now it’s semi-long-distance, she’s cold sometimes, avoids communication, rary engages with my interests, and I’m tired of putting in all the effort — don’t know what to do tbh.