Or how do moderators do this?
Does the site feature image-searches for this purpose?
Or check the images with the same tag(s) manually column by column?

I'm pretty sure if you pulled the thing youre uploading from the same source then the site blocks you from posting it anyway

Even so, you can even check the artist and characters tag.

For example, I uploaded this yesterday:
hypnohub.net/post/show/70...tomless-butt_plug-fake_an

So I check ranmabooks (artist) and then ranma saotome tags.