Thankfully, there is a module for that, but the documentation isn’t great.

1. Install the Views Node Access Filter module
2. Edit the Content view (URL: example.com/admin/structure/views/view/content, UI Path: Structure > Views > Content > Edit)
   
3. With Default display selected, click add a Filter Criteria
   
4. Check Editable and click Add and configure filter criteria
   
5. Click Apply
   
6. Save the view
   

Now the Content view will only show the user the content that they are able to edit.