Is it permissible for an employee who books airline tickets to personally contract with companies that his own company has rejected (in order to achieve his goal), while bearing the responsibility for non-payment, and to obtain a personal profit in addition to the company's profit?

The employee is an agent of the company. If the company forbids him from contracting with a certain party, he is not allowed to do so. If he profits from such a contract without the company's knowledge, then he is consuming illicit gain (haram) and has betrayed the trust, because an agent does not have the right to act without the permission of his principal. Therefore, he must repent to Allah Almighty and cease this action, because, as a private employee, he is not permitted to work for anyone other than his employer during the period of employment, except with the employer's permission. If what he does serves the company's interest, he should present the matter to them. If they approve his action and the liability rests on his shoulders, then there is no harm; otherwise, there is.