Talk to your partner about what they consider romantic activities, because everyone has a different idea of what is or is not romantic. It can also depend on other bits of context. For example, going to a fancy dinner with one friend might be seen as romantic by your partner, but a fancy dinner with a sibling or group of friends might not be.
The timing could also be a bigger factor than the activity itself. Your partner might feel offended that you chose to leave the birthday celebration/activities for personal time to relax and unwind, only to then go and do something with a different friend. Even if that activity with the other friend wasn't seen as a romantic activity, your partner might have still been upset that they were perceived as a lower priority on their birthday, a day they might have expected to be more prioritized by them.
Even further, different people have different degrees of, for lack of a better term here, jealousy towards their partner in regards to activities. I'm not implying your partner is toxic or a jealous sort, but a lunch "date" with a friend is acceptable for some partners, but crosses the line for others.