I can't believe it took a whole month of trial and error just to find the right hardware... There's also an audio cassette player and a VCR incoming. Meanwhile:
The piece that actually does the analog to digital conversion: a composite video to HDMI adapter and converter. The SCART head in the back can take RCA or S-video contacts. The weakest link in the whole setup, because a professional person would probably use an expensive expansion card inside their computer or the likes..
The capture card. It takes digital video and/or audio signals through an HDMI connection and sends it to the computers via USB-C. Perhaps the second weakest link, since - again - a pro would probably do the conversion with a fancy PCIe card.
My beloved TASCAM. The only piece that I already had in my possession. Instead of letting the above capture card capture the analog audio, I let this do that. Do read up on TASCAM! They have a pretty long and reputable history within audio.
This little handheld video camera will playback Mini DV cassettes. I have already captured two of them successfully. Oh boi, do I love the second hand market.
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