[US] Very weird or very good job recruiting scam or maybe legit

Wife received an email over the weekend from someone claiming to be an independent recruiter head-hunting for a senior role at a company she and I both worked at for years. We’ve had an email conversation for three days. If it’s a scam, I’m struggling to understand its purpose.

Red flags:

• Sent from a personal Gmail address
• Found a corresponding LinkedIn account (not verified) with no posts.
• Google and reverse image searches don’t confirm their identity but don’t reveal anything negative.
• Never claims to be able to have a direct phone call.

Green or beige flags:

• The posting in the emails looks and sounds legitimate, though it’s for a job not currently posted.
• The posting is for a senior, director-level position within my wife’s knowledge and experience.
• The posting uses unique verbiage and formatting typical of the company.
• The initial email was sent directly to my wife’s personal email, not via a job site.
• The “recruiter” hasn’t asked for personal information, pressured her to move to WhatsApp or other chat apps, asked for money, or done anything I’d consider a scam target.
• The emails are well-written, professional, and natural-sounding, with responses to various questions.
• The initial email was detailed and looked like a real recruiter’s email.
• The only request she’s made is for her resume, and now a cover letter and executive summary brief
• there has been no pressure or requests for anything more than these

Here’s the thing: if this was a scam, what’s the goal here? Everything so far is proceeding like a normal recruitment process. Yet, part of me still feels like it is and I just haven’t figured out what their goal is yet.

Any thoughts on this?