Is it obligatory to delay prayer until the time of the Iqamah or shortly before it, instead of going to it at the time of the Adhan, if the employer is bothered by going at the time of the Adhan?

You must follow the employer's instruction because you are an employee, and the contract requires your commitment to work hours. Since the employer does not object to you leaving a little before the prayer is established, this is good for attaining the reward of the congregation. The employer is not obligated to permit you to pray in congregation unless you stipulated that in the contract. You have the choice between adhering to the employer's instruction or leaving the job if you do not like it. You must make up the prayers you missed for decades, according to the majority of scholars.