Salaam, need advice about ghusl when intention was unclear

Hey, So last night I had a wet dream but when I woke up it was kind of fuzzy in my memory. Later I took a normal shower, but I made sure to wash my entire body completely-like every part, not just a quick wash. At the time, my intention was just to get clean overall, not specifically thinking 'this is ghusl,' because honestly, I hadn't fully registered that I was in need of ghusl at that moment. After the shower, I performed wudu too. Now I’m overthinking a bit: does that shower qualify as ghusl even though my intention wasn’t focused on it? Or do I have to do it again? It's confusing because I definitely washed everything properly, just didn't start out with the clear thought of it being ghusl. If anyone has some insight, jazakAllah khair, it would really help clear things up.