I want to filter a list based on the page the list is on...

Add a Project Field to your document library either managed metadata or choice field and add values for all types of projects.

Create Multiple views for document library and setup the filter with the condition for project field value to b equal to specific project and make sure only content relevant to specific project shows up in each view.

Add Document library webpart on all the project pages and change the view to render view specific to the project.

To update the view of a web part on each project page, please try the steps below:

In the page where the web part is, click the gear on the upper right corner>Edit page>Edit Web Part> Expand the Selected View, choose the specific project view you want to use.> Click Apply to check the outcome>Click OK and save the changes.

Hope this helps!