MSSQL - convert list of datetimes in a date range
Your problem is known as an "Islands and Gaps" problem. As far as I can see your solutions is correct (given that I understood what you try to achieve) up until:

,LEAD(StartDate,1,StartDate) OVER(ORDER BY StartDate) AS EndDate


Why are you replacing the EndDate you calculated in MinMax? Try:

SELECT
    [UserId], [RoomId], [TypeId]
    ,StartDate  
    ,EndDate
FROM
    MinMax
ORDER BY
    StartDate
   ,EndDate


Regarding how you calculate the group, I assume that a reservation is for the same room, and type during the whole period. You may want to consider something like:

,ROW_NUMBER() OVER (PARTITION BY [RoomId], [TypeId] 
                    ORDER BY [Date] ASC)
-ROW_NUMBER() OVER (PARTITION BY [UserId], [RoomId], [TypeId] 
                    ORDER BY [Date] ASC) AS Grp


In your query, GRP changes regardless of which room or type that interferes with the enumeration of dates.

PS. Welcome to the forum. A Very good first question. If GRP puzzles you, I suggest that you look at the row_number functions individually, before looking at their difference DS.  

EDIT:

The idea you used uses the fact that some other user interrupts the current ordering, and thereby creates a new grp. Since several users can rent the room at the same time, I don't think that will work. Here is one idea (date is a reserved word so I changed it to dt to be able to get rid of the annoying quotes []):

with start_period as (
    select a.userid, a.roomid, a.typeid, a.dt as start_date 
    from Reservations a
    where not exists (
        select 1 from Reservations b
        where a.userid = b.userid
          and a.roomid = b.roomid
          and a.typeid = b.typeid
          and a.dt = dateadd(day, 1, b.dt)
    )
), end_period as (
    select a.userid, a.roomid, a.typeid, a.dt as end_date 
    from Reservations a
    where not exists (
        select 1 from Reservations b
        where a.userid = b.userid
          and a.roomid = b.roomid
          and a.typeid = b.typeid
          and a.dt = dateadd(day, -1, b.dt)
    )
)  
select x.userid, x.roomid, x.typeid, x.start_date
     , min(y.end_date) as end_date
from start_period x
join end_period y
    on x.userid = y.userid
    and x.roomid = y.roomid
    and x.typeid = y.typeid
    and x.start_date &lt;= y.end_date
group by x.userid, x.roomid, x.typeid, x.start_date;

1   1   2   2020-04-01T00:00:00Z    2020-04-03T00:00:00Z
1   1   2   2020-04-05T00:00:00Z    2020-04-07T00:00:00Z
1   1   2   2020-04-10T00:00:00Z    2020-04-10T00:00:00Z
2   1   2   2020-04-01T00:00:00Z    2020-04-03T00:00:00Z
2   1   2   2020-04-05T00:00:00Z    2020-04-05T00:00:00Z
2   1   3   2020-04-06T00:00:00Z    2020-04-07T00:00:00Z


Fiddle

The idea is pretty simple, get all dates (for a given user, room, type) where there is no predecessor. Then get all dates (for a given user, room, type) where there is no successor. For all start_dates, find the smallest end_date that is bigger than the start_date