does delivery happen closer to EDD or the date given by the sonographer at the growth.scan?

The most accurate edd would be that given in your first scan. The scans done later on have a variability of up to 2-3 weeks. typically the date by lmp and usg will be less than 15 days apart

The delivery or rather onset of labor is expected closer to the sonography date. This is because the sonography is as per the growth observation. It shows the readiness of the baby.