SQL Server 2019

By using db<>fiddle, you agree to license everything you submit by Creative Commons CC0.
create table t (name varchar(10), date_from date, date_to date);
insert into t (name, date_from, date_to) values
  ('A', '2022-01-03', '2022-01-03'),
  ('A', '2021-12-29', '2021-12-31'),
  ('A', '2021-12-28', '2021-12-28'),
  ('A', '2021-12-27', '2021-12-27'),
  ('A', '2021-12-23', '2021-12-24'),
  ('A', '2021-11-08', '2021-11-09');
6 rows affected

with extended as (
    select name,
        date_from,
        case when datepart(weekday, date_to) = 6 then dateadd(day, 2, date_to) else date_to end as date_to
    from t
), adjacent as (
    select *,
        case when dateadd(day, 1,
            lag(date_to) over (partition by name order by date_from)) = date_from then 0 else 1 end as brk
    from extended
), blocked as (
    select *, sum(brk) over (partition by name order by date_from) as grp
    from adjacent
)
select name, min(date_from), max(date_to) from blocked
group by name, grp


name
(No column name)
(No column name)


A
2021-11-08
2021-11-09

A
2021-12-23
2022-01-03