TLDR: You have to re-create the content types using the correct parent content type!
You cannot change the parent content type of a content type:
- The Parent property is read-only.
- The content type ID is prefixed with the parent content type's ID. See explanation below copied from here. This is for SP 2010 but it works the same for SP 2013 and later versions of SharePoint, including SP Online.
Content type IDs uniquely identify the content type and are designed
to be recursive. The content type ID encapsulates that content type's
lineage, or the line of parent content types from which the content
type inherits. Each content type ID contains the ID of the parent
content type, which in turn contains the ID of that content type's
parent, and so on, ultimately back to and including the System content
type ID. SharePoint Foundation uses this information to determine the
relationship between content types and for push-down operations.
You can construct a valid content type ID using one of two
conventions:
- Parent content type ID + two hexadecimal values (the two hexadecimal
values cannot be "00")
- Parent content type ID + "00" + hexadecimal GUID