Total Sum by Column (Matrix)

Please provide sanitized sample data that fully covers your issue. If you paste the data into a table in your post or use one of the file services it will be easier to work with. Avoid posting screenshots of your source data if possible.

https://community.powerbi.com/t5/Desktop/How-to-Get-Your-Question-Answered-Quickly/m-p/1447523

All done in Power Query, although probably the part of the grant calculation can be done more easily in the BI desktop environment.

if source is your tab,

then open an empty query and paste the following code ovewriting all.

let

Start_End = (SD, ED, optional Culture as nullable text) as table => 
  let
    StartDate= Date.FromText(SD,[Format="dddd d MMMM yyyy", Culture=Culture]),
    EndDate= Date.FromText(ED,[Format="dddd d MMMM yyyy", Culture=Culture]),
    DayCount = Duration.Days(Duration.From(EndDate - StartDate))+1, 
    Source = List.Dates(StartDate,DayCount,#duration(1,0,0,0)), 
    TableFromList = Table.FromList(Source, Splitter.SplitByNothing()),    
    ChangedType = Table.TransformColumnTypes(TableFromList,{{"Column1", type date}}), 
    RenamedColumns = Table.RenameColumns(ChangedType,{{"Column1", "Date"}}),
    res= Table.AddColumn(RenamedColumns, "gant", each 1)
  in 
    res,

     #"Grouped Rows" = Table.Group(source, {"Category", "Name", "Task Type", "Assigned To"}, {"from to", each Start_End([Start Date]{0},[Expected End Date]{0},"it-IT")}),
    #"Expanded from to" = Table.ExpandTableColumn(#"Grouped Rows", "from to", {"Date", "gant"}, {"Date", "gant"}),
    #"Pivoted Column" = Table.Pivot(Table.TransformColumnTypes(#"Expanded from to", {{"Date", type text}}, "it-IT"), List.Distinct(Table.TransformColumnTypes(#"Expanded from to", {{"Date", type text}}, "it-IT")[Date]), "Date", "gant", List.Sum),
    #"Grouped Rows1" = Table.Group(#"Expanded from to", {"Date"}, {{"total", each List.Sum([gant]), type number}}),
    #"Transposed Table" = Table.Transpose(#"Grouped Rows1"),
     GranTotal = Table.PromoteHeaders(#"Transposed Table", [PromoteAllScalars=true])
      in 
      Table.Combine({#"Pivoted Column",GranTotal})

Thank you for providing the sample data.

Please remember that in a matrix visual each measure is calculated four times. Once for the individual cells, but then also for the Column totals, the row totals , and finally for the Grand Total.

Accordingly your measure will need to take all these scenarios into account. Your current formula only works for the cells.

Note:  your "all('Date'[Date])" filter is not providing any help as your tables are disconnected (which they need to be for your scenario). 

There are also some typos in your code. Here's a cleaned-up version

column values = 
VAR _startdate = min('sample data'[Start Date])
var _enddate = max('sample data'[Expected End Date])
var _status = max('sample data'[Current Status])
var _period = min('Date'[Date]) >= _startdate && max('Date'[Date])<=_enddate

return switch(true(),
        _period && _status = "Complete",1,
        _period && _status = "In progress",2,
        _period && _status = "Overdue",3,
        _period && _status = "On Hold",4,
        _period && _status = "Yet to start",5)

Now the question is - what result do you expect for the Column subtotals? Do they make sense in your scenario?