A project should never be done at the expense of one of the partners. Equality between partners, in this case the festival organizers and the project organizations, is crucial for a successful project. Both sides should have ownership and should encompass the project. It is not the obligation or duty of any of the partners to do such a project. Both sides should understand the project, and each should evaluate if it fits into their own values and needs. Check your partner's website early on to find out more about their values.
There should be some kind of written deal that defines the partnership for both sides – it doesn't matter if it's a barter deal or if there's money involved.
Find inspiration in Portuguese Boom festival’s vision:https://boomfestival.org/boom2023/vision/
Or in Edinburgh Festival’s information about their values and the city’s local and global positioning: https://www.edinburghfestivalcity.com/about