To be eligible under the VCSP, you must have filed all required Forms 1099 for the previous 3 years for the workers you want to reclassify. If I filed Forms 1099 late, am I still eligible for the VCSP

Yes, you may still be eligible for the Voluntary Classification Settlement Program (VCSP) if you filed the required Forms 1099 late, provided that the forms were filed within 6 months of their due date (including extensions). If you meet this condition and all other eligibility requirements, you can participate in the VCSP. However, if you filed the required Forms 1099 more than 6 months after their due date (including extensions) or did not file them at all, you would not be eligible for the VCSP.

Sources:
Instructions for Form 8952 (11/2023)
Publication 15 (2024)
IRM Part 4. Examining Process. Chapter 23. Employment Tax. Section 20. Voluntary Classification Settlement Program (VCSP) Procedures
IRM Part 4. Examining Process. Chapter 23. Employment Tax. Section 6. Classification Settlement Program (CSP)