If you like engineering stick to it. Develop deeper expertise. Pay will never be an issue.
If you don't want to be an engineer, then move to engineering adjacent roles - PM being one. MBA is not required for PM, though if done from a reputed institution opens up lot of doors. MBA is a networking degree... Access is what is sold in the name of course. You could gain the business knowledge thru just books and real world experience.
MBA makes a lot of sense of you want to change your trajectory or switch careers. It makes less sense if you just want to progress in current one. Don't do an MBA without any experience.
You should be able to justify to yourself, the cost of MBA + opportunity costs of not working vs expected growth ROI for MBA.