Is it permissible, from a Sharia perspective, for an employer to prevent an employee from working in the same field after leaving the job, without specifying a duration or having a written contract, knowing that the employee had verbally promised not to compete with the company in its markets and with its clients?

It is permissible for an employee who has resigned from their job to work in a field similar to their previous company's activity, to benefit from their experiences, and to deal with their former clients, unless there is a condition preventing that, or a disclosure of business secrets. As long as you will be working in different markets and with different clients, there is no harm upon you.