My best advice (as someone also prone to anxiety) would be to focus on your coping strategies. If you have relaxation techniques take time to yourself to practice them, if not then research some. Everyone is different, find what works for you.

I have to be honest, from what you write he seems like he's just got a lot on - of course I can't know for sure, just how it seems in writing. Also we all differ in how much contact we need with SOs, this may just be his preference, it's for you to decide whether it's a deal breaker or not.

I tend to get anxious (in friendships rather than my long term partnership), second guessing when people don't get in touch. Generally driving myself crazy. I have to work on this, what helps is keeping busy, social events, sport, volunteering, getting outside my own head. Not meaning to be patronising, this may or may not apply to you, take what you want from it. Take care, hope you can find something that works for you.