My code idea, if we use the native new item directly, it will be difficult to transfer the title value between the two pages, so I used SP.UI.ModalDialog.showModalDialog().
Code in parent list display form:parentlistdisplayformcode.txt
Code in child list new form:childlistnewformcode.txt
My test result for your reference:
Tip:Don't forget to change the url of new from to that of your environment.