Yes, the DJI Mic Mini is compatible with the Sony ZV-1 Mark II.
Sony ZV-1 Mark II has a native 3.5mm Mic Terminal (confirmed on Sony's own spec page). DJI Mic Mini ships with a 3.5mm TRS camera cable, which plugs directly into that terminal -- no adapter or accessory needed.
“Mic Terminal Yes (3.5 mm Stereo minijack)”
“DJI Mic Mini Camera Audio Cable (3.5mm TRS) × 1 DJI Mic Mini Mobile Phone Adapter (Type-C) × 1”
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Confidence: high confidence