In order to get the non-DCT lossy compression, you need to request "Modular Mode" in the program that compresses the image. But for some reason I don't know, Irfanview is literally hiding that checkbox from you, and you can enable the feature by editing the dialog resource and making the checkbox no longer hidden.
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Meanwhile, I still prefer WEBP for lossless compression, because the decompression code is so fast. In terms of who has the best lossless compression, WEBP and JXL easily beat AVIF, and JXL usually beats WEBP, but not always. In one case, I saw a grayscale BMP file getting better compression with FLAC (!) than JXL.
WEBP's lossy format is just not that good, AVIF and JXL beat the hell out of it, sometimes the JPEG even looks better. But WEBP's lossless format is excellent.