Does the FAA keep a public registery of pilots?

John Travolta famously used to pilot his own private 707 back when he had it. I seem to recall hearing he actually has a private pilot’s license with a 707 type rating. If so, he might be the only person in the world with that combo. I could look it up, but I have to run to a meeting in a minute…

I’m back an hour later, and yep, he does:

Certificate: PRIVATE PILOT
Date of Issue: 3/28/2022

Ratings:
PRIVATE PILOT
AIRPLANE SINGLE ENGINE LAND
AIRPLANE MULTIENGINE LAND
INSTRUMENT AIRPLANE

Type Ratings:

P/B-707 P/B-720 P/B-737 P/CE-500 P/CL-600
P/DA-50 P/DA-2000 P/EA-500S P/G-1159 P/HS-125
P/LR-JET

Limits:
ENGLISH PROFICIENT.
B-737 B-707 DA-50 DA-2000 SIC PRIVILEGES ONLY.
AUTHORIZED EXPERIMENTAL AIRCRAFT: SO-G2.
CE-500 (VFR ONLY).