The requirements for ESA and PIP are very different (even where they appear similar!), it is perfectly possible to be in receipt of Enhanced components of PIP and work full time, for instance.
You will certainly not be routinely moved to the Support Group as a result of your PIP award.
If you are not too late to request a reconsideration of your ESA, you can certainly use the PIP award in support but it would be up to you to show how this applies to the ESA descriptors.
Otherwise, you can use the report as evidence when your ESA is reassessed - but you would still have to demonstrate how it applies to the descriptors.
Nothing on this board constitutes legal advice - always consult a professional about specific problems