Tests say I am an introvert but I genuinely like being around people. What is going on?

Both things are true and they are not in conflict. You have run into a case where the word has drifted from what the scales measure.

In everyday use, introvert has come to mean something like "needs recovery time after social contact". In trait terms, extraversion is mostly about reward sensitivity to social and novel stimulation — how much pull the company has, how much you seek it out, how positive and energetic you run in it. Those two are related but far from the same, and you can straightforwardly be high on the enjoyment and high on the recovery cost. That combination is common and it is exactly what you have described.

What you are calling introversion is closer to the cost side, and it deserves to be measured separately, because the cost has more than one source. It might be sensory load, or the effort of managing how you come across, or a low tolerance for unpredictability in the room. Those feel similar from the inside and they call for different accommodations — a quieter venue, a shorter stay, or knowing the guest list in advance.

The distinction worth ruling out: if the recovery time is mostly relief that it went acceptably, and you spend part of it reviewing what you said, that points at social anxiety rather than a cost of stimulation. Enjoying people and dreading being evaluated by them coexist very comfortably, and they are different things to address. A scale that scores contact cost, self-monitoring, and post-event rumination separately will tell you which one you are carrying — and that is a far more actionable answer than which side of the introversion line you fell on.