In lossy mode I think there is no difference between AVIF, HEIC or JXL. AVIF is even a little bit ahead.
For lossless mode, JXL's fast modes (-e1 and -e2) are fast. But their compression ratio is terrible. The higher levels are not usable in a camera in terms of speed.
Of course, my favorite and many people's favorite in this regard is HALIC (High Availability Lossless Image Compression). It is a speed/compression monster. The problem is that for now it is closed source and there is no Google or similar company behind it.
For lossless mode, JXL's fast modes (-e1 and -e2) are fast. But their compression ratio is terrible. The higher levels are not usable in a camera in terms of speed. Of course, my favorite and many people's favorite in this regard is HALIC (High Availability Lossless Image Compression). It is a speed/compression monster. The problem is that for now it is closed source and there is no Google or similar company behind it.