I think your insecurity and anxiety is probably being signaled because you noticed a negative change in his behavior.  He went from doing things that you liked and appreciated to now not doing those things, and that sends up red flags, leading to anxiety/insecurity.  I get what he’s saying about not wanting to text all day, every day because that really is time consuming, but it says something to me that he sometimes doesn’t reply until the next day. Unless you’re sending him messages after he goes to bed, he could at least give you a response before he goes to sleep, especially if he knows you like the goodnight texts.

It IS a good sign that he’s taking you to shows with friends and that he’s going out of his way to see you, but his flaking in both text and hanging out is not a good sign, so, if I were you, I think I would just back off a little bit and don’t expect anything or get further attached until you feel confident in his interest in you. You can definitely keep hanging out with him and see where things go, but just sort of detach yourself a bit from the outcome of this if you can. I know that’s hard when you really like someone, but I think that’ll help with your anxiety. If you find you’re getting too attached and unable to detach and feeling more anxiety because of it, then, yeah, I would leave the situation because he might not really be a match for you if your affection/communication styles are clashing or if you’re not on the same page. And if you pull back and he steps up to the plate and draws himself closer, then you can see how you feel and go from there.