avif also supports lossless, but it's so inefficient it might as well not exist.

Lossless webp is a completely different image format compared to lossy webp, even though they come under the same file extension. Unlike lossy webp, it's a good image format that has excellent compression ratio compared to png. I've often been using it for screenshots to avoid damaging text clarity and still maintain acceptable file size.

jxl has excellent support for both lossy and lossless cases, and can replace both lossy avif (even if somewhat less efficient at low file sizes), and lossless webp.

Note also that converting jpeg to jxl is 100% reversible, you can convert it back to exactly the same image (byte for byte identical) if you need to.