with
starts as (
    select 
        p.*
        , case when p.start_date = lag(p.end_date, 1, null) over (order by p.start_date) then 0 else 1 end as proj_start
    from projects p
)

, grps as (
    select start_date
        , end_date
        , sum(proj_start) over (order by start_date asc) as grp_num
    from starts
)

select
    min(start_date)
    ,max(end_date)
from grps
group by grp_num
order by datediff(day, min(start_date), max(end_date)) asc, min(start_date) asc