Effects of vaccine damage payment on PIP/contribution based ESA Support group

I'd be very grateful if someone can help me with this query:

I am getting higher rate PIP and Contribution-based ESA (Support Group.)
I've been advised to apply for Vaccine Damage Payment as my condition might have been triggered by a vaccination.
On the Gov.UK website it says that the Vaccine Damage Payment can affect benefits.
Please can someone tell me if I am awarded the vaccine Damage Payment, will it affect my higher rate PIP payments and the Contribution-based ESA Support Group payments in terms of any backdated deductions from the Vaccine Damage Payment or my benefits being paid out moving forward.
Many thanks