I was out of work for 3 months this year on FMLA and received short term disability payments for maybe 1/3 of that time. Does this count as “paid family leave”

No. FMLA is unpaid so it can't be considered paid family leave. However, the portion you got paid for may be Paid Family Leave.

• See What is Paid Family Leave (PFL)?

 

The 1993 Family and Medical Leave Act (FMLA) entitles eligible employees to take an unpaid, job-protected leave of up to 12 workweeks in a 12-month period for family- and medical-related reasons.

 

Related Information:

• Where do I report a 1099-G for unemployment or paid family leave?
• Is maternity or parental leave considered paid family leave?
• Is sick pay the same thing as paid family leave?
• Is medical leave or short-term/long-term disability considered paid family leave?

At some employers that would be a paid medical leave.