The Referer header in the image request must be set to https://www.pixiv.net/.

You can test it yourself with curl "https://i.pximg.net/c/250x250_80_a2/img-master/img/2020/04/29/05/21/46/81142134_p0_square1200.jpg" -H "Referer:https://www.pixiv.net/"

I don't think we have any logic for that in SearXNG yet, so it would require some refactoring to the image proxy, but in theory we could use the image proxy to set that header for this engine. However, the engine won't be usable without the image proxy of the instance being enabled.

reminder for myself:

with this modification to webapp.py, this engine works (when the image proxy is enabled):

    request_headers = {
        'User-Agent': gen_useragent(),
        'Accept': 'image/webp,*/*',
        'Referer': 'https://www.pixiv.net/', #added this line!
        'Accept-Encoding': 'gzip, deflate',
        'Sec-GPC': '1',
        'DNT': '1',
    }

i'll try doing some more work on this later.