Is it crazy to reach out again for a role I previously didn't get?

Earlier this year, I applied for an Analyst role after reaching out to the team director. He was kind enough to include me in the hiring process, but I didn't make it past the first round, which was a bit embarrassing at the time. It’s been about six months since then, and I’ve noticed that his team is recruiting again for a similar position at my level.

Would it be crazy or wrong to reach out to him again? I’m considering highlighting my growth since our last interaction and expressing my continued interest in his team (though I'm in a different vertical/industry). Essentially, I’d like to show that I’ve been working on my skills and would love another chance to be considered.

What do you all think? Is this a good approach, and how should I phrase it?

edit: just wanted to add we never spoke just over email so i am not really close to the man