Couple things here. First, don't use characters like hash symbols in your column names. It means you have to always quote those column names, and it's completely unnecessary.

Second, I sincerely hope this is just some sort of weird report formatting you're doing because you physically can't do it on the front end. If this is a persisted storage format, you need to rethink your design.

That out of the way, you just need to string_agg your fields together. The oddity in your results however is that you want to concatenate all the SrNo values except for the SrNo on the current row. This means you're going to have to join your data to itself on the email where the SrNo values differ.

I'd recommend you NOT store this in a dedicated field (i.e. doing an update) and that you just project this when you're querying the data out. But regardless, here's how you could do it both ways. Note I'm assuming SrNo is a unique key on the table.

drop table if exists #data
;with a (SrNo, Email, DupNo) as
(
    select 4117, '[email protected]', cast(null as varchar(max)) union all
    select 4366, '[email protected]', null union all
    select 4493, '[email protected]', null union all
    select 90210, '[email protected]', null union all
    select 1234, '[email protected]', null union all
    select 0, '[email protected]', null
)
select *
into #data
from a 

-- To just select 
;with dups as
(
    select
        AnchorSRNo = a.SrNo,
        Email = a.Email,
        DupSrNo = b.SrNo
    from #data a
    inner join #data b
        on a.Email = b.Email
            and a.SrNo != b.SrNo
)
select 
    o.*,
    DupNos = 
    (
        select string_agg(DupSrNo, ',')
        from dups i
        where o.SrNo = i.AnchorSrNo
    )
from #data o

-- To perform an update
;with dups as
(
    select
        AnchorSRNo = a.SrNo,
        Email = a.Email,
        DupSrNo = b.SrNo
    from #data a
    inner join #data b
        on a.Email = b.Email
            and a.SrNo != b.SrNo
)
update t
set DupNo = (
    select string_agg(DupSrNo, ',')
    from dups i
    where t.SrNo = i.AnchorSrNo
)
from #data t
inner join dups d
    on t.SrNo = d.AnchorSrNo

db<>fiddle