Is it permissible to withdraw from accepting a new job offer after giving one's word to a recruitment company, and accepting a counter-offer from the current company, knowing that the actual signing of the contract has not yet taken place?

Your statement to the recruitment company representative, "I will accept immediately, even if my current company gives me a counter-offer," is a promise. It is recommended to fulfill it, but it is not obligatory according to the majority of scholars.

The Hanafis are of the opinion that a promise is not legally binding unless it is conditional.

As for the Malikis, there is a narration among them that a promise to contract is legally binding on the promisor if the promisee incurs a financial obligation based on that promise.

The Hanbalis have explicitly stated that fulfilling a promise is not legally obligatory.

The ruling of the Shafi'is, which considers breaking a promise detestable, implies that the one who breaks the promise cannot be forced to fulfill it.

Therefore, according to the majority of scholars, you are not obligated to accept this job, and you may remain with your current company.