Managed migration to UC .

Hi,
I have had a few days of major concern, 're my private pension payments, and after ......finally.... Getting through the DWP switchboard after 1 hour 40 mins, have received positive clarity from them about my situation. I receive contribution based ESA, topped up with income based ESA. I have been on ESA since 2013.
I also am in the support group,and have all the various severe disability components.
I started receiving a very small pension 6 years ago ( at age 56) and because the sum was far smaller than the contribution based ESA limit of £85 per week, ( I receive £130 per calender month), I never worried about it. I spoke to them today and told them my exact up to date calender month payments for 2025, and they confirmed that I did not owe anything, and had nothing to pay back.
My question is, I am aiming to do my migration at the end of April,(it has to be by mid may) how do I receive what I currently receive, when it's only my income based ESA and HB that are being moved across. If I was only receiving income based ESA, all my pension money would be taken as income, and I would be £130 per month worse off. Will I get this as part of a top up on migration, or will I get it via a separate payment from "new style ESA?
Many thanks , Chris.
I apologise if this is all very confusing,