SQL Server : replace Null values with values from the same column by matching values in a different column

You can use an updatable CTE:

with toupdate as (
      select t.*, max(date) over (partition by id) as max_date
      from t
     )
update toupdate
    set date = max_date
    where date is null;

update a
SET a.date = b.date
from #test AS a
INNER JOIN (SELECT * FROM #test WHERE platform = 'web') as b on a.id = b.id
WHERE a.date is null

Update the tablename #test as needed.

A correlated subquery should work

declare @table table (platform char(3), [date] date, id int)
insert into @table
values
('web','2018-10-10',1),
('mob',null,1),
('mob',null,1),
('web','2018-10-15',2),
('mob',null,2),
('ntl','2018-10-09',3),
('web','2018-10-12',3),
('web','2018-10-11',4),
('mob',null,3)

update @table
set date = (select max(date) from @table t2 where t2.id = [@table].id)
where [@table].date is null  

select * from @table

I would not recommend naming a column date as it's a reserved word, but this will give you the desired result assuming there is only 1 web entry per id.

UPDATE a
SET [date] = b.[date]
FROM MyTable a
INNER JOIN MyTable b ON a.id = b.id and b.platform = 'web'
WHERE a.platform = 'mob' AND a.[date] IS NULL

You can do like

UPDATE T
SET [Date] = D
FROM
(
    SELECT ID, MAX([Date]) AS D
    FROM T
    WHERE [Date] IS NOT NULL
    GROUP BY ID
) TT INNER JOIN T ON T.ID = TT.ID
WHERE T.[Date] IS NULL;

db<>fiddle demo