Well, BGP and HEIC (or rather HEIF as HEIC is just the container IIRC) uses HEVC which means royalties, so unless MPEGLA were to make images using HEVC royalty free, I can't see any scenario where it would replace jpeg.
Webp is royalty free, but for lossy compression it's not a good enough improvement (imo) over jpeg for it to replace it. For lossless compression though, it beats PNG both in size and compression/decompression speed by a good margin.
And the other one I find very interesting is PIK, which is a new lossy/lossless codec that is supposedly a good improvement over jpeg while being very fast, and also has the feature of being able to losslessly recompress jpeg images into pik with ~20% compression: https://github.com/google/pik
There is JPEG XL, and image format from EVC. Which is the purposed Royalty Free Video Codec from MPEG. ( All while VVC, the successor of HEVC is racing ahead.... )
Webp is royalty free, but for lossy compression it's not a good enough improvement (imo) over jpeg for it to replace it. For lossless compression though, it beats PNG both in size and compression/decompression speed by a good margin.
As for potential jpeg replacements, we have AVIF which is like BGP,HEIF but with the royalty free AV1 codec: https://aomediacodec.github.io/av1-avif/
And the other one I find very interesting is PIK, which is a new lossy/lossless codec that is supposedly a good improvement over jpeg while being very fast, and also has the feature of being able to losslessly recompress jpeg images into pik with ~20% compression: https://github.com/google/pik