Edit: perhaps I got this wrong. Maybe they meant staff engineer as in very senior IC who does not manage? If this is the case your role is to be strategic. You might write production code, you might design architecture. Whatever your current project(s) they will have wide reaching business impact. Asking difficult questions that may make people uncomfortable is very much part of this role. Yes these roles are seldom hired in to by first timers. But once you've be in one before, being hired externally is possible. I have a hard time believing that this person could do this type role at this point in their career (yes it was 2020 so adjust accordingly).

I'll leave the below since it might be useful for someone seeking a mid-level career.

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I think they are equating a staff engineer with a mid-level engineer. They say that companies don't hire for this role but in my 26 years of working this has not been my experience. Granted, I focused on < 1000 employee companies because I liked the transparency, mobility, and influence I had there.

I don't know what kind of role they were looking for, but not wanting to write production code in a software company usually means you are going to be in a support role. These are often not traditional software engineering roles. You don't have to have a college degree, but you need to know the material. Programming is a skill just like anything. You have to practice.

Interviewing is an inexact, unfair process. Keep trying, doing as many as your sensitivity to rejection allows.

The thing that many applicants don't know is that many parts of a positions requirements that seem fixed are actually flexible.

Focus on good communication skills, listen well, and demonstrate concretely how you exemplify the skills they're looking for. Often the how and the why matter more then the what.

Recruiters usually know very little about what they're searching for. Yet they are the first line filter. Say what ever you need to say to move past them. But be mindful that they will often report what you say to the interview panel or hiring manager. Telling them an outright lie can be a bad idea.

Leetcode exercises aren't fun and they're a time sink. You can and should practice for them. In many cases they are a first line screen to filter out the noncoders. If you're considering searching for a solution and cutting and pasting it as your answer, know that leetcode has basic tools to detect this. They track your time and keystrokes.

Most teams have a balance of dead weight, followers, doers, and leaders. There are usually more of the former than the later. This plays in your favor if looking for a mid-level role.

Good luck out there.