Where did the phrase "I found Jesus" originate from? And how come it has carried on for such a long time??

Not a historian, but I believe Sojourner Truth is probably one of the names most closely associated with the phrase.

https://en.wikipedia.org/wiki/Sojourner_Truth

Phrases like "I found Jesus" or "y'all need Jesus" have a lot of longevity because they describe a sentiment of experiencing salvation and reconciliation in terms that are understood by a large part of the population.

Instead of "Jesus" you could say "I found my purpose in life" or "I found love" and I think you'd be expressing nearly the same sentiment.

When people ask me if I’ve found him, I ask “Why, if he’s so important, do you keep losing him?”

Probably not the root of what you're looking for, but when I was growing up in the 70s there was a national Christian campaign called the "I Found It* campaign. The church I grew up in participated and I Found It yard signs and buttons and billboards and radio ads and TV ads sprouted every where.

Of course the answer to *what did you find?" Was always Jesus, or eternal life or something like that.