2004 was when it was popularized in business speak. MBAs were going on all about it and it was all over business journals. it didn't pass out of business speak around that time then, because that was before social media. nobody was blogging about emotional intelligence in 2006, other than business people writing for other business people. It was popularized in a 2004 article in the Harvard Business review, specifically, wherein the article quoted the psych researcher who wrote a book about from the 90s. It was MBAs scraping around for a made up metric by which to evaluate effective managers and how to choose/promote managers, and this was the 'new metric' they put forth. It was very trendy at the time to talk about business leaders needing to be empathic, which was part of George Bush's whole 'compassionate conservatism/neoliberalism' movement that the corpos latched onto at the time (like the latch onto Trumpism today). It all was a big nothing burger and by the time Obama came around it was completely gone and corpos were back to focusing on the bottom line and freaking out about how evil Democrats were.
it didn't become common to see laypeople use it in everyday language until the past few years. now it's on literally every other dating profile and social media post where the person blathers on about how they have high emotional intelligence and it's everyone else who doesn't and they only want to associate with other high emotionally intelligence people... it's a bullshit status marker.
lest us not forget, before 'emotional intelligence' it was emotionally quotient (EQ) in the 2010s. everyone was blathering about 'I have high EQ' 10 years ago. because again, another buzzword trying to sound legitimate by equating itself to IQ. Nobody uses that term anymore because it became passe, emotional intelligence is the replacement for it.
EQ/emotional intelligent/butthole empathy was never anything measurable or standarized. It's nothing more than a buzzword that is hyped up as the 'answer' to everything, when it is in fact, a meaningless empty term that allows people to project anything they want.
in 5 years nobody will use this term anymore. there will be a new one, or maybe they will revive EQ. it's all marketing in the end, about conning folks into believing something is real and selling them the idea of it so they buy your book, view your channel, or subscribe to your stream. etc