You can be happy and serious at the same time. It’s not a contradiction. If you look at the photos of Rav Elyashiv ZTZ”L, you’ll notice that he never smiled. That doesn’t mean that he wasn’t happy. Far from it. He had an internal simchah from his own personal Avodas Hashem.
Even though we are genuinely sad during the 3 weeks (or try to be), we can still be satisfied deep down that we are mourning the way Hashem wants us to.
It’s just a a different type of simchah than the one we show in times like Yomtov, or on Purim.