My question back to you is this: Why do you want to be in Consulting & specifically MBB?
If this is your dream, you can get there through other routes. Join BIG4/Accenture, prove yourself and move to MBB. Or join a tech firm/Amazon/FG/Google/Start-up, clock some relevant experience and then move to MBB. And there are other options too..
Also, any consultant who is not Tech/IT Savvy will become irrelevant in a few years, if they already are not. Management consultants who dont understand AI, ML, Agile (scrum, kanban), DevOps,Design Thinking will be useless. So you are in a great position to be very close to this part of the Technology landscape as we live in a tech driven world. Consulting projects are becoming more and more tech driven.
So, I think you need some help to improve your positioning/branding and justifying your transferrable skill set. Nothing wrong in your IT PM role, but some works needs to be done to articulate your story, skills better.
Happy to chat more, so feel free to shoot me a personal message.