IGNOU has an international reputation because it serves over 3 million students and offers over 200 courses. It is the world's largest university. In the long run, their curriculum is worthwhile, and there are very few negative reviews on IGNOU MBA online.
Symbiosis, IMT, and NMIMS each have their unique value and attractiveness in terms of employment. Regardless, if you end up learning the subject to the best of your ability, the university name serves only as decoration on top of the dish.
MBAs are well-suited to leadership roles such as managing a team. Your decision to work in your chosen field of engineering, where you will learn concepts such as how a company hierarchy works, its SOP, customer service, and so on, is a good one. This will provide you with a fresh perspective on the value and/or necessity of an MBA.
Work experience combined with an MBA from a government-approved university will be extremely beneficial (SMU is a big no-go area). Work experience always provides more comprehensive and valuable knowledge than books and degrees. Pursue excellence, and success will always follow.