" The best case scenario is that they say something like "Oh, probably just doing X with my friends," which makes it clear that you won't be really expected to join in or participate—which is fine.

You aren't that serious yet, so preferring to spend a birthday with friends is totally normal. Possibly, your date will mention a party or get-together to which you'll be invited.

If he or she mentions their upcoming birthday in passing, you should casually ask: "Fun, how are you planning to celebrate?

I'm just now torn if I should just go the "typical" route of a cologne and b-day card or something where he can make as much as he wants and it's fresher and side note healthier.

It just may not be something he uses "all the time" like possibly cologne which he also really likes...

My cousin told me I shouldn’t be upset or think anything of it, since the relationship was so new (yes, two days old “officially,” but we had been dating for four months).

I let it go because I didn’t think it was worth getting upset over, but two months later, while I am feeling a bit under-appreciated in other aspects of the relationship, I’m a bit bothered by this.