Search on Compound docs children

As a user, I want to search for compound document files in my instance. For this, I need a new filter:

Acceptance criteria:

• I can search specifically for, or filter out, compound docs. Outcome: filter and only have results on the compound doc facet, or file types (materials, product design, 3d objects, etc...)
• As a user, I need to know if my item is a parent, child or both

•  I can search across compound doc children files only, or only parent compounds that contain a child file
• As a user, I want to search only for a child

How the search works when searching for a parent or child with example

• Tshirt (parent) + tissue rouge (child)
• Chapeau (parent) + tissue rouge (child)
• Jeans (parent) + tissue blue (child)
• Costume (parent) avec chemise (Parent &child) avec tissue rouge(child)
  (in this case, chemise is both Parent and Child)

List of fields:

full text
Tags
Authors
Collection
modification date
coverage
size

Can we have:
Content type (empty if we dont have any) (if we create extension like materials for example)
Created
State