filter doesn't impact the matrix visual properly

Here is a slightly different approach to get your desired result.

1.  Keep your original Table query and your DAX table called "first status" (maybe rename it because it is used for more than that in this approach)

2.  Have no relationship between the tables

3. Make two slicers for extraction date and status from the first status table

4.  Use this measure in your matrix

Projects =
CALCULATE (
    DISTINCTCOUNT ( 'Table'[project id] ),
    TREATAS ( VALUES ( 'first status'[extraction date] ), 'Table'[extraction date] ),
    TREATAS ( VALUES ( 'first status'[status] ), 'Table'[status] )
)

Your users can multi-select (Ctrl-Click) in either/both slicers to show the projects that meet the criteria.  It takes out the first/second part.  If this doesn't work, there is a more complex version that can be written that will make sure all the selected values are true for the given project (e.g., both status values are present for that project).  But I thought I would suggest this simpler one first to see if it met your needs.

If this works for you, please mark it as the solution.  Kudos are appreciated too.  Please let me know if not.

Regards,

Pat