Dateadd to exclude weekends

You could use CASE in the addition bit e.g.

declare @start date = '2020-01-01'
declare @end date = dateadd(dd, 10, @start)
declare @daystoadd int = 3
;WITH sampledatelist AS
(
    SELECT  @start AS datum
    UNION ALL
    SELECT  dateadd(DAY, 1, datum)
    FROM    sampledatelist
    WHERE dateadd(day, 1, datum) < @end
)

The CTE above just generates some dates. Here is the query that finds the next working day

select datum, -- the date we're trying to add to
DATEADD(DD, @daystoadd, datum) 
     AS JustAddedOn, -- as it says on the tin
DATEPART(DW, DATEADD(DD, @daystoadd, datum)) 
     AS DayOfJustAddedOn, -- what day of the week would that be
CASE WHEN DATEPART(DW, DATEADD(DD, @daystoadd, datum)) = 7 THEN 
      DATEADD(DD, @DAYSTOADD + 2, DATUM)	-- Handle Saturdays
WHEN DATEPART(DW, DATEADD(DD, @daystoadd, datum)) = 1 THEN 
      DATEADD(DD, @DAYSTOADD + 1, DATUM)	-- Handle Sundays
ELSE 
      DATEADD(DD, @daystoadd, datum) -- otherwise use the JustAddedOn date
END as calcdate
from sampledatelist

which gives results

datum		JustAddedOn	Day	calcdate
2020-01-01	2020-01-04	7	2020-01-06
2020-01-02	2020-01-05	1	2020-01-06
2020-01-03	2020-01-06	2	2020-01-06
2020-01-04	2020-01-07	3	2020-01-07
2020-01-05	2020-01-08	4	2020-01-08
2020-01-06	2020-01-09	5	2020-01-09
2020-01-07	2020-01-10	6	2020-01-10
2020-01-08	2020-01-11	7	2020-01-13
2020-01-09	2020-01-12	1	2020-01-13
2020-01-10	2020-01-13	2	2020-01-13

Caveats
- check your localisation settings for what constitutes a weekend for your part of the world!
- This doesn't handle national holidays etc

Incidentally, I personally intensely dislike converting dates to strings just to add a time (that's just a me thing). I prefer to add the required number of hours (or in this case seconds) to the "start" of the day in question e.g.

declare @starttime INT = DATEDIFF(SECOND,0,CAST('08:00:00' AS datetime)) -- End Time will be 1 second earlier

select dateadd(second, @starttime, dateadd(dd, datediff(dd, 0, dateadd(day, -5, current_timestamp)), 0)) as [Start Date],
       dateadd(second, @starttime - 1, dateadd(dd, datediff(dd, 0, dateadd(day, -4, current_timestamp)), 0)) as [End Date]

Lastly, if I was doing a lot of comparing dates with workdays and holidays I would build up a date table containing all the useful stuff such as date, day of the week, quarter, financial period, working day etc etc then use that a reference in other queries, joining on date. You could even have a pre-calculated "next working day" column