Add rows accumulated by current month

You can UNPIVOT your data, use the window function sum() over() to calculate the running total and then PIVOT the results.

Example

Select *
 From  (
        Select Year
              ,Channels
              ,Col
              ,Amt
         From TEST_CHANNEL_YTD A
         Cross Apply ( 
                      Select Col
                            ,Amt = sum(Amt) over (Order by Seq)
                       From (values ('Jan to Jan',1,Jan)
                                   ,('Jan to Feb',2,Feb)
                                   ,('Jan to Mar',3,Mar)
                                   ,('Jan to Apr',4,Apr)
                                   ,('Jan to May',5,May)
                                   ,('Jan to Jun',6,Jun)
                                   ,('Jan to Jul',7,Jul)
                                   ,('Jan to Aug',8,Aug)
                                   ,('Jan to Sep',9,Sep)
                                   ,('Jan to Oct',10,Oct)
                                   ,('Jan to Nov',11,Nov)
                                   ,('Jan to Dec',12,Dec)
                               ) V (Col,Seq,Amt)
                        ) B
       ) src 
 Pivot ( sum(Amt) for Col in ([Jan to Jan],[Jan to Feb],[Jan to Mar],[Jan to Apr],[Jan to May],[Jan to Jun],[Jan to Jul],[Jan to Aug],[Jan to Sep],[Jan to Oct],[Jan to Nov],[Jan to Dec]) ) pvt

Results

You can go for CROSS APPLY and conditional grouping as given below:

declare @table table(year int, channel char(10), jan int,feb int, mar int, apr int, may int, jun int, jul int, aug int, sep int, oct int, nov int, dec int)

insert into @table 
values
(2021,'channel1',1193,11,5,2,2,5,0,0,0,0,0,0),
(2021,'channel2',3228,373,156,106,76,86,17,13,0,0,0,0);

select year, channel,
sum(case when mnumber <= 1 then ca.mvalue end) as [Jan To Jan],
sum(case when mnumber <= 2 then ca.mvalue end) as [Jan To Feb],
sum(case when mnumber <= 3 then ca.mvalue end) as [Jan To Mar] ,
sum(case when mnumber <= 4 then ca.mvalue end) as [Jan To Apr],
sum(case when mnumber <= 5 then ca.mvalue end) as [Jan To May] ,
sum(case when mnumber <= 6 then ca.mvalue end) as [Jan To Jun],
sum(case when mnumber <= 7 then ca.mvalue end) as [Jan To Jul] ,
sum(case when mnumber <= 8 then ca.mvalue end) as [Jan To Aug],
sum(case when mnumber <= 9 then ca.mvalue end) as [Jan To Sep], 
sum(case when mnumber <= 10 then ca.mvalue end) as [Jan To Oct],
sum(case when mnumber <= 11 then ca.mvalue end) as [Jan To Nov], 
sum(case when mnumber <= 12 then ca.mvalue end) as [Jan To Dec]
from @table as t
cross apply
(values
(1,t.jan),
(2,t.feb),
(3,t.mar),
(4,t.apr),
(5,t.may),
(6,t.jun), 
(7,t.jul), 
(8,t.aug), 
(9,t.sep), 
(10,t.oct),
(11,t.nov),
(12,t.dec))as ca(mnumber,mvalue)
group by year, channel