I think you both need help reaching a deeper understanding for what the other is trying to say.
The problem I'm seeing is that you're communicating about things, events on the surface level, but you're not adequately communicating about the underlying dynamics, the structural problems, and you're getting defensive and hurt when confronted with what your partner has to say, rather than truly hearing it and showing compassion (which isn't the same as agreeing with them).
When people start a conversation with you-statements (you don't care about me, you don't put any effort in, you never listen to me, ...), that triggers instant defense-mechanisms. Because the other will be temped to defend themselves and prove that these allegations are false.
Starting with I-statements (I feel sad about the way we've been communicating. I feel lonely in this relationship. I don't feel seen, ...) already softens the message. Then, it's up to the partner to not instantly jump to their own defense, but to engage in what was said. To be curious, and to want to understand the problem.
How long have you been feeling this way?
How do I do to contribute to that feeling?
When do I not make you feel this way? What do I do to make you feel better?
How can we help each other communicate differently?
The trick is to look at any and every problem in your relationship not as a me vs you problem. But a me and you together vs the problem.
If he feels neglected, that is a shared problem. You two are the team handling this problem together. Pointing a finger and assigning blame has no place in that conversation.
The conversation you should have been having was this:
Him: I feel anxious because I'm afraid that despite our tough conversations, I worry that nothing will change between us.
You: Why do you worry about this? Did I do something do make you feel this way?
Him: I needed an appology from you, to feel validated. And that hasn't happened. It feels as though we're just carrying on as before, despite the painful things that have been said.
You: I understand how an appology can make the difference. I've tried to show you in my own way that I care by cooking for you and making that effort. But I understand that you needed me to actually say 'I'm sorry'.
Him: Thank you for saying that. I understand you made an effort in your own way and I do appreciate that though.
This is how you have mutually validating conversations. Taking accountability for your own contributions to the problem, and also showing empathy for how your partner is feeling.