I [India,31F] and my SO [UK,29M] just completed one month together but complications are rearing their heads.

I'm basically posting what I've posted on Reddit. But haven't received many responses. I'm looking for more perspectives before I take a decision.

A bit of background:

We met through online chat exactly one month back. Within the first few hours of chat, we felt attracted to each other and barely 24 hours had passed that we confessed our love to each other (I know that's crazy and a giant red flag for most people, but it just happened for us).

He is sweet, caring, and lovable. I have a demanding job and he's been understanding enough to work things around my schedule. But as much as I love him and want to be with him, there are a few things that are making me clueless. I'd love for all you amazing people here on this forum to help me with your honest advice, insights and suggestions.

1. Communication

He is an introvert -- which I initially read as being someone who takes time to open up. For the first three of weeks, he kept a wonderful pace of communication. Though I should also mention here that he's not comfortable with phone calls (we've tried 3-4 times but he mostly remained silent during calls and later apologized for being shy and awkward). He is OK with video calls, though we always mute ourselves and chat via text even while on Skype.

For the first three weeks or so, he would text me multiple times a day, staying up late at night for me, even leaving romantic messages when I'm sleeping or at work and all of that. After which, he's slowed down to the point where I have to initiate most conversations and even then, he seems unable to communicate in anything more than one-liners.

Now, I completely understand his need for space and alone time. So I'm wondering if this is a 'recharge' phase he's going through as he might have exhausted himself in the first few weeks?

2. His depression

He suffers from depression. I got to know this within 10 days of meeting him when he tried to shut himself down and went into a shell, wanting to cry, feeling useless etc. But even then, he didn't block me out completely and allowed me to help him out and make him feel better.

Of late, after he has quietened down, I feel he broods more, keeps to himself, and even looks sad. He has problems that he doesn't share and feels bogged down by them. I want to help but can't do anything about it. Also because of his introversion, I don't feel convincing him to talk is a good idea. So I try to leave him on his own and that leads to...

3. My anxiety

I'm a jittery and anxious person esp when it comes to personal relationships and I constantly worry and overthink things. The fact that he doesn't share his problems with me makes me feel distanced. On telling him this, his answer was "please babe don't worry. I'll tell you if there's something to worry about. Trust me please." (sic)

I'm not quite convinced because from his actions, it seems like something is bothering him constantly. (Or am I overthinking?)

Sometimes I crave a conversation or just want to ask him about his day, but feel discouraged thinking that I might be stepping on his personal space where he's seeking refuge or recharging himself. What's making things worse is, I can't talk to him about how I'm feeling cause that will probably make him feel worse about himself (I once cried to him about a personal problem and for the next couple of days, he was all down and feeling guilty that he can't even hug me to make me feel better).

Honestly, I feel extremely attracted and connected to him, love him, and truly hope we can stay together. He feels the same and even the thought of us breaking up makes him all sad and mopey. I'm a bit overwhelmed and clueless as to how to proceed (totally willing to go the extra mile) without compromising the emotional well-being of both of us.

Please feel free to offer your honest advice.

Tl/DR:

In LDR with an introvert, dealing with a lack of communication and depression. Need advice on how to move forward.