Connection between the Date Column in two different data source is not working - Slicer doesn't work

You need to create a couple of dimension tables and link them to your fact tables. Firstly, create a proper date table, marked as a date table. Delete the relationships between your fact tables and create one-to-many relationships from your date table to each fact table.

Then create another dimension table for your project names. You can do this in Power Query by combining the columns from each sheet into a new table and then removing duplicates, or you could do it in DAX like

Project Names =
DISTINCT (
    UNION (
        DISTINCT ( 'Audit'[Project Name] ),
        DISTINCT ( 'Statistics'[Project name] )
    )
)

Then create one-to-many relationships from the new dimension table to each fact table.

Use columns from the dimension tables in your visuals, slicers etc and everything should filter correctly.