No, the DJI RS 3 Mini is not compatible with the Sony Alpha A9 III.
Sony A9 III body weighs 703g (with battery+card, per Sony's own Help Guide). Paired with a Tamron 150-500mm F5-6.7 Di III VC VXD lens (1,725g for Sony E-mount, per Tamron's own product page) -- a realistic pairing for this sports-flagship body -- combined weight is ~2,428g. DJI RS 3 Mini's stated payload capacity is up to 2kg (4.4lbs) per DJI's own product page. 2,428g exceeds that capacity by ~21%; the gimbal cannot safely balance or support this combination.
What works instead
See all compatible gimbal for the DJI RS 3 Mini →“Mass (Approx.) 703 g (1 lb 8.8 oz) (including battery pack, SD card)”
“Weight 1,725g/60.8oz (w/o tripod mount) (Sony), 1,710g/60.3oz (w/o tripod mount) (Fujifilm), 1,720g/60.7oz (w/o tripod mount) (Nikon), tripod mount 155g/5.5o”
“RS 3 Mini possesses a load capacity of up to 2 kg (4.4 lbs), enabling a wide range of camera and lens combinations.”
Last verified:
Confidence: high confidence