No, the DJI RS 4 Mini is not compatible with the Sony Alpha 1.
Sony Alpha 1 body weighs 737g (with battery+card, per Sony's own Help Guide). Paired with a Sigma 150-600mm F5-6.3 DG DN OS | Sports lens (2,100g, per Sigma's own product page) -- a realistic pairing for the wildlife/sports work this flagship body is built for -- combined weight is ~2,837g. DJI RS 4 Mini's stated payload capacity is 2kg (4.4lbs) per DJI's own product page. 2,837g exceeds that capacity by over 40%; the gimbal cannot safely balance or support this combination.
What works instead
See all compatible gimbal for the DJI RS 4 Mini →“Mass (Approx.) 737 g (1 lb 10.0 oz) (including battery pack, SD card)”
“Sony E-mount: 2,100g / 74.1 oz. (Tripod socket included)”
“2kg/4.4lbs Payload for Camera and Phone It supports a wide range of mainstream mirrorless cameras and lens combinations, lightweight vlog cams,”
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Confidence: high confidence