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Guetzli was already mentioned and roughly does what you are talking about.
MozJPEG [1] includes several quantization tables that are optimized for different contexts (see the quant-table flag and source code for specific tables[2]), and the default quantization table has been optimized to outperform the recommended quantization tables in the original JPEG spec (Annex K).
It's also worth noting that MozJPEG uses Trellis quantization [3] to help improve quality without a per-image brute force quantization table search. Basically rather than determining an optimal quantization table for the image, it minimizes rate distortion on a per-block level by tuning the quantized coefficients.
[1] https://github.com/mozilla/mozjpeg
[2] https://github.com/mozilla/mozjpeg/blob/5c6a0f0971edf1ed3cf3...
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Well, if we're talking about web, then I it's better to use WebP rather than PNG.
It's widely supported by vendors if you do not need to deal with IE: https://caniuse.com/?search=webp.
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