Saw this situation on LI and had similar issue so I wanted to share:

When a recruiter or hiring managers sees something like "Team Lead", they automatically think technical lead with no reports. When they see Engineering Manager, they think managing a team.

If your company does not align job titles with the market, you'll lose out on opportunities, plain and simple. Recruiters and ATS quickly scan for fit and if the terms aren't there, you're gonna get passed up.

Your comp is going to be impacted severely as well. Wonder why you're downleveled? Probably a combination of your title, size of team/scope of projects, and company tier.

From what I have experienced, I've had 2 eng manager positions and 1 sr. eng manager position although my titles have been "Engineering Team Lead" (previous) and "Engineering Manager" (present). I've since changed my titles on my resume and profiles to reflect this because who is going to audit my job titles anyway?