[NEOS-1062] Update instances of useFormPersist to use the local copy

[nickzelei]

Copy what we've done in the AiGenerate new Schema form to use the new local version of useFormPersist along with nesting it inside of a child componenet.

This is way more performant and fixes a lot of unnecessary re-renders that are happening in those forms.

_{From SyncLinear.com | NEOS-1062}