No, but the original chart is missing some key elements to make you jump to the conclusion those are the only elements that matter. Such is not the case, though.
The stock market is up because risk premium got increasingly cheaper and earnings improved, the job market is down because of oversaturation in white collar sectors (and finance and tech specifically, since they are the heavy weights, and they overhired in 2020). Moreover, as you can even see in the original chart itself, the job market started to deteriorate before ChatGPT was even a thing, since the hiring freezes in 22Q1 were due to rate uncertainty