when it comes to others' birthdays we should recognize and respect how valuable they are to the other person, not our own values. What I mean is, a good friend, even if they don't feel birthdays are important will go out of their way for the friend that feels they are because after all it's a celebration of their personal birthday and being a friend is about giving something to others. So it should not be a dilemma in your mind. If you were to tell a friend that you didn't give them something or call them or what not because you don't find birthdays important, it's risking making them feel like you are telling them their values are not important.

You didn't do that, but just forgot it, and I think your gesture was commendable and probably appreciated by them.

I think that your issue is likely something you should work out with your therapist though, like you said.