What was the name of leadership training in the Air Force for E-4 (back when E-4 were Senior Airmans and before they became E-4 Sergeants?

Depends on the time frame you are referring to. When I was a SrA before gaining NCO status as a Sergeant, we had the NCO Preparatory Course (I completed the course in June of 1988). At that time it was 2 weeks long. My supervisor at the time went to what was called Level 1 PME if I recall correctly.

Before they started promoting Staff Sergeants at such a high rate, SRA without line numbers were allowed and encouraged/directed to attend ALS- Airman Leadership School. It was required to promote to SSgt.

SrA. Just a short tale. I went to Airman's Leadership School back in the 60's. 4 weeks long and to many gigs and spend the week-end restricted. Long days, tough inspections and lots of marching. Learning experience. Probably finished about half the way down. Approx 5 or 6 years later, NCOA. 6th in class ranking. Very new TSgt. Schools were by commands back in the day.. Got one gig in NCOA.