I have a work around so you do not have to create a relationship.

If you just want to be able to select a project on a dropdown and see the budget and the partners ID, I would just link the tables by a combined field name and use a slicer.

If you have a field with an identical name and data type, Looker should link the 2 together automatically so that if you add a slicer to one it will filter the other table as well.

If the fields do not automatically join you can create a calculated field in each data table that references the ID you want to use and name the field IDs with exactly the same name.