Viewing another projects fields in parent projects list view

I am a software architect responsible for scoping & assigning various tasks to three different teams within my department, so I want to have a parent project that allows me to create tasks, list out requirements, and sort them into sections in the parent project. I have rules set up to add these tasks to the individual team boards once they are added to these sections in the parent project. Within these individual team boards (we view them as kanban boards so we can drag tasks between different statuses like todo, in progress, etc) we have a custom field called Status that correlates to these sections. Is there any way to view custom fields from these individual teams’ boards in the parent board in the list view?

Yep! You just need to have the custom field be an organization-wide field (i.e. based in your custom fields library), not a project-specific custom field. You can read about the two different types here:

You can then select to include it in both projects from your library.