HEIF, AVIF and JPEG XL all support multi-layer images, so you could e.g. encode the background in a lossy layer (which works well on blurry stuff) and foregroun

HEIF, AVIF and JPEG XL all support multi-layer images, so you could e.g. encode the background in a lossy layer (which works well on blurry stuff) and foreground in a lossless layer (which works well on screenshots).