Build a timeline based on separate tables with multiple dateFrom and DateTo columns?

I have two tables, tblPrice and tblDiscount, each have their value with a liveFrom and liveUntil column (plus some other columns but I'm leaving those out to try and make this more straightforward).

What I'm trying to do is display a list of prices and discounts as an ordered list which will show how prices have changed based on the price changing or the discount changing.

tblPrice

tblDiscount

expected result

Things to note are:

• Prices don't necessarily run continuously (note row 1 and 2 on tblPrice have no difference in price, it just happened to be ended and then restarted at a later date so this would give a period where there was no active price for the product).
• we're focusing on prices but a discount can be live while a price is not so in that situation the effective live from date would still need to be that of the price and not the discount.
• a price could be active without a discount so the effective discount would be 0

I've tried joining the tables on each other based on a date range and then using a case statement to show the live from and live until dates but it just doesn't seem right and I just can't quite get the logic. The results aren't coming up how I'd hope and I feel I'm going down a rabbit hole in the wrong direction.

My query so far (which as said I'm not sure is the right way to go) is:

SELECT
    P.[priceID],
    P.[retailPrice],
    P.[liveFrom],
    P.[liveUntil],
    D.[logID],
    D.[discount],
    D.[liveFrom],
    D.[liveUntil],
    ------------
    CASE
        WHEN SDV.[liveFrom] <= P.[liveFrom] AND (SDV.[liveUntil] >= P.[liveFrom] OR SDV.[liveUntil] IS NULL) THEN
            SDV.[liveFrom]
        WHEN SDV.[liveFrom] >= P.[liveFrom] AND (SDV.[liveUntil] <= P.[liveUntil] OR P.[liveUntil] IS NULL) THEN
            P.[liveFrom]
        ELSE
            '1900-01-01 00:00:00'
    END AS [EFFECTIVE_FROM],
    CASE
        WHEN ISNULL(P.[liveUntil],@date) < ISNULL(SDV.[liveUntil],@date) THEN
            P.[liveUntil]
        ELSE
            SDV.[liveUntil]
    END AS [EFFECTIVE_UNTIL]
FROM 
    tblPrice P
    INNER JOIN tblDiscount D ON P.[supplierDiscountID] = D.[supplierDiscountID]
        AND ((
                D.[liveFrom] <= P.[liveFrom] 
                AND (D.[liveUntil] >= P.[liveFrom] OR D.[liveUntil] IS NULL) 
            ) OR
            (
                D.[liveFrom] >= P.[liveFrom]
                AND (D.[liveFrom] <= P.[liveUntil] OR P.[liveUntil] IS NULL)
            ))
ORDER BY
    P.[liveFrom],
    D.[liveFrom];

I'm not getting the results I'm wanting and the route I'm going down just doesn't seem right. Can anybody give me any pointers or ideas please?

You have to look for discount rows that begins before the price ends and ends after the price begins, so this could be a way to do it:

-- Sample data
declare @tblPrice table
    ( priceID int not null, retailPrice money not null
    , liveFrom datetime not null, liveUntil datetime)
declare @tblDiscount table
    ( logID int not null, discount decimal(5,4) not null
    , liveFrom datetime not null, liveUntil datetime)
insert into @tblPrice values
     ( 446413,1666.33,'2022-01-31T11:36:21.490','2022-04-08T15:13:41.230')
    ,(1338193,1666.33,'2022-04-09T09:30:14.043','2023-04-05T09:37:21.767')
    ,(2707357,1749.65,'2023-04-05T09:37:21.767', null)
insert into @tblDiscount values
     (192, 0.37, '2022-01-31T11:27:45.060','2023-01-09T14:32:24.413')
    ,(498, 0.32, '2023-01-09T14:32:24.413','2023-04-11T15:40:06.460')
    ,(639, 0.317,'2023-04-11T15:40:06.460', null)

-- Prices with discounts available or without any discount
select P.retailPrice
    , isNull(D.discount, 0) as discount
    , case when P.liveFrom  >= isNull(D.liveFrom, P.liveFrom)
        then P.liveFrom
        else D.liveFrom
      end as liveFrom
    , case when P.liveUntil <= isNull(D.liveUntil, P.liveUntil)
        then P.liveUntil
        else D.liveUntil
      end as liveUntil
from @tblPrice P
left join @tblDiscount D on
     -- P.supplierDiscountID = D.supplierDiscountID and
     D.liveFrom <= isNull(P.liveUntil, getDate())
 and P.liveFrom <= isNull(D.liveUntil, getDate())

union all
-- Prices that begins before 1st discount available
select x.retailPrice
    , 0 as discount
    , x.liveFrom
    , x.lf as liveUntil
from (
select P.retailPrice, P.liveFrom
    , min(D.liveFrom) lf
from @tblPrice P
left join @tblDiscount D on
     -- P.supplierDiscountID = D.supplierDiscountID and
     D.liveFrom <= isNull(P.liveUntil, getDate())
 and P.liveFrom <= isNull(D.liveUntil, getDate())
group by P.priceID, P.retailPrice, P.liveFrom
having min(D.liveFrom)
     > P.liveFrom
) x

union all
-- Prices that ends after last discount available
select x.retailPrice
    , 0 as discount
    , x.lu as liveFrom
    , x.liveUntil
from (
select P.retailPrice, P.liveUntil
    , max(isNull(D.liveUntil, getDate())) lu
from @tblPrice P
left join @tblDiscount D on
     -- P.supplierDiscountID = D.supplierDiscountID and
     D.liveFrom <= isNull(P.liveUntil, getDate())
 and P.liveFrom <= isNull(D.liveUntil, getDate())
group by P.priceID, P.retailPrice, P.liveUntil
having max(isNull(D.liveUntil, getDate()))
     < isNull(P.liveUntil, getDate())
) x

order by liveFrom