For corporate dev / strategy, would an MBA be worth it after 3 years in IBD?

Hi everyone! Happy New Year!

I recently had to leave my top tier BB after 3 years due to visa issue and have been wondering if I should look at an MBA as the next step. I have been interested in trying out corporate development or PE but due to visa issue I haven't had the chance to recruit during my 3 years in IB.

My understanding is that the traditional path is 3 years in top BB -> 2 years in top PE -> HSW or M7 in general -> post-MBA PE associate / VP role. Since I don't currently have any experience in PE at all and only have 3 years of work experience, I am not sure if I will truly benefit from a top tier MBA program as the post-MBA PE roles almost always require pre-MBA PE experience. Honestly, if, after getting my MBA, I need to compete with current BB analysts for *PRE-MBA" associate roles, would pursuing this degree be worth the time and resources at all?

Also, like I said, I think I have an interest in trying out PE but am not entirely positive that I will like the experience / be good at it. So if I eventually decide to pursue other finance routes such as corporate development / strategy / corporate finance, would an MBA be of substantial value? I understand an MBA is incredibly helpful for anyone who wants to switch into finance without prior experience, so I would appreciate any insights on how much it can help in my case given my goals and background.

Thank you!
Smalltown