The cliff notes version is that JPEG and JPEG XL don't encode pixel values, they encode the discrete cosine transform (like a Fourier transform) of the 2d pixel grid. So what's really stored is more like the frequency and amplitude of change of pixels than individual pixel values, and the compression comes from the insight that some combinations of frequency and amplitude of color change are much more perceptible than others

In addition to the other comments: you can have an internal memory representation of data be Float32, but on disk, this is encoded through some form of entropy encoding. Typically, some of the earlier steps is preparation for the entropy-encoder: you make the data more amenable to entropy-encoding through rearrangement that's either fully reversible (lossless), or near-reversible (lossy).

No, JPEG is not a bitmap format.

The gradient is stored, not the points on the gradient