Edit searchable fields in Task view

Hey there!
I’m new to ERPNext (not new to ERP, Software Customization or googling what I can’t solve myself).
Just set up my first installation for a private project and added some “Projects” and assigned some “Tasks” to it. Now, when I try to edit a task and assign it to another project, the search only works on the project key (PROJ-####). Which I find very unhandy, because I think you’d normally want to search for the project name:

Searching for the project name works on other views, though.

Can anybody help with this?

Best
Dominik

Just adding a screenshot that shows a view in which the project name works as search key.

Can anybody help?