I wonder if it would be good to just sit him down and let him know how much it means to you that he remembers your birthday, and ask him why he forgets it.
Maybe he doesnt believe in celebrations like birthdays, like how some people feel that Valentines day and other special days are just a marketing ploy to sell more stuff. Maybe he's just forgetful, and just needs to put a reminder somewhere to remember to wish you a happy birthday every year on the day.
I think that even if a person doesnt hold much meaning in birthdays, if they really care about your feelings, they will make an effort to make you happy. Although at 30+, he should have developed the maturity by now to understand this about relationships.
I dont believe that this in itself is a dealbreaker although it may be for you. It is possibly a red flag though. You need to look at the big picture. How does he treat you overall?
I know exactly what it's like because the same thing happened to me. With what i am about to tell you, I dont recommend that you follow my example or have it influence what you choose to do, but i will share my experiences just so that you can see what happened in my life.
My ex was very stubborn to the point that his beliefs not to celebrate birthdays was more important than keeping his partner happy. He was 35. However celebrating birthdays was also not a big deal for me and he was good in other ways so i didnt mind that much. I could deal without celebrating birthdays. I just still wanted to do something nice and low key on the day.
It started off with him forgetting my birthday two years in a row. On the third year, i hinted about my birthday coming up, but he was passive aggressive which upset me. I dont know if he knew it was my birthday or not. He didn't wish me happy birthday. On the fourth year, i just explicitly reminded him the day before and on the day so he definitely knew. Still he was too stubborn to wish me a happy birthday and i was upset that he treated the day as an ordinary day. I was all dressed up to go somewhere special with him (no booking, just a walkin restaurant) as i wanted to celebrate the occassion, but he wasn't feeling like it and he wanted to get MacDonalds for lunch. Takeaway too. Through the drive thru. On the fifth year, i decided not to have him stop me from being happy on my birthday and i did my own thing all on my own, excluding him, and i was happy. I bought myself a cake that i love and treated myself. I also stopped doing nice things for him on his birthday, as i had been doing every year. He noticed the absence, and i guess that may have been the point where it awakened him. Unfortunately it was too late. For other reasons, he is now my ex.
All people have good and bad traits so don't take my personal experience to heart. Relationships will not always be rosey. They work not just because of love, but because when there is conflict, they are committed to working it out together, and can do so compatibly. People change and grow over time. I would recommend that you think rationally and clearly see who he is as a person and whether he is compatible with you. Best of luck to you.