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Some Sony cameras support acting as webcams natively over USB now too, so you can skip the HDMI step. Not sure about which specific models though

The list is here: https://support.d-imaging.sony.co.jp/app/webcam/en/download/ It weirdly includes a5100 and not a6000, which are internally almost identical.

Also at least for older cameras it’s 720p only, no fullhd, so you’re still better with hdmi adapter.