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JPEG compression is standardized. The only part of the algorithm that is configurable is the quantization matrix which is essentially a control of what information to throw away and how much. So unless you are throwing away a huge amount of information (really shitty image), there is no way a different library will somehow save you a bunch of space.
That is exactly what's happening :) better quantization matrix results in 25% smaller files with the same perception-based q which makes webp kinda useless often https://siipo.la/blog/is-webp-really-better-than-jpeg
Try jpeg-xl though. it's amazing.
Mozjpeg performs 2 tricks to improve compression: