I'm more interested to hear why 9? Why not 3 or 12. What's going on there? I've been on both sides of the fence and it's interesting to hear thoughts on it always.
Hiring is the most important thing you are doing in a company. Always has been. From my experience it's also highly dependent on how big the org is and how structured it is. No two hiring processes are alike. Common theme I've picked up when hiring people is first and foremost to do a 'vibe check' convo through which both you and the applicant get to know a bit each other, ambitions, learn about the role and do a q&a. If you have experience with this, and you know your team(s), you will easily pick up if the person fits the bill. That usually takes around an hour to two _at most_. Second part is then for the person to talk to the team itself, the team lead. Over time, I found it's best to do a live exercise of either walking through something or doing something (not leet code, just something representative as a mental exercise) while chit chatting about it which is also a covert vibe check. If that passes, third convo is back to the same person initially talked to to strike a deal (which was foreshadowed with terms on the first talk). All in all 3-4 hours total after years of pruning.
Personally - vibe check, vibe check, vibe check. Never let HR do the talk, let HR funnel candidates for a shopping list.. or in this case it seems to be essays that do that.