Yes, the DJI RS 4 Mini is compatible with the Sony ZV-1 Mark II.
Sony ZV-1 Mark II has a fixed (non-interchangeable) lens, so its full operating weight -- 292g including battery and card, per Sony's own spec page -- is exact. DJI RS 4 Mini's stated payload capacity is 2kg (4.4lbs) per DJI's own product page. 292g is well within that range, so the camera balances and operates normally with no adapter or special setup required.
“Weight (with battery and memory card included) Approx. 292 g (10.3 oz)”
“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