It's a reference to one of the most culturally important stories in Buddhist countries. Not knowing about it is like consuming English media without knowing anything about Shakespeare's plays.

The English name is Journey to the West and the monkey is Sun Wukong in Chinese or Son Goku in Japanese. You might notice the main character in Dragon Ball Z has the same name, but the monkey king is referenced constantly in all sorts of Eastern media. The synopsis and main characters sections in that Wikipedia link will give you the general idea, but I would recommend reading or watching any of the versions to get a better understanding of the vibe.

Your metaphor is basically just calling them arrogant and reckless, lacking a good strategy and rushing in to things.

No kind of expert on the idiomatic use, but the literal translation makes it feel like the monkey is going after something without a plan for where to land. I would expect it to indicate impulsivity

It has a lot of meanings.

The oldest one I know of is that of Monkey King, who in the ancient story stole and ate the peaches of immortality. He did this without any plan; in some versions he was hungry and didn't understand that it would make him immortal. This act of spontaneity also inconvenienced the peach owner, who had intended to serve the peaches to those who were worthy of them.

Since then various martial arts moves and stories and so on were named after that one little bit of the story, usually to showcase a combination of spontaneity and strength.

Mistral 8×7B that I have in front of me now says "A monkey that jumped out to pluck a peach" is often translated as "to jump the gun" in English, and refers to someone that is too eager to take an immediate but inappropriate step.

~~It also says the idiom is from the classical text "The Analects of Confucius, Book 12"~~

This is a smart offline open source model, but like everything AI, - citation needed as this is not a valid primary source.

Some Google searching shows that the monkey King in "Journey to the West" ate peaches that gave him immortality. Google also shows a martial arts move where you grab the opponent's testicles.

It's probably a chengyu, but I don't know what story it's from.

Some people need to watch some Monkey. It's a 70s TV adaptation of the "Journey to the west".

After school viewing for me in the UK.