Recursively Conditionally get parent Id - sql

Question

I have two tables: Budget Line and Expense. They are structured in such a way that an expense must have either a parent record in the budget line table, or a parent record in the expense table. I need to select all child-most expenses for each budget line.
For example - BudgetLine:
Id
Description
1
TEST123
2
OTHERTEST
Expense:
Id
ParentId
ParentType
Description
1
1
BudgetLine
Group of Expenses
2
1
Expense
Expense # 1
3
1
Expense
Expense # 2
4
2
BudgetLine
Expense 3
Desired result:
BudgetLineId
ExpenseId
Description
1
2
Expense # 1
1
3
Expense # 2
2
4
Expense # 3
I am looking to omit expenses in the result only if they are the only sub-child. Note that an expense may have many children, grandchildren, etc.
I have tried the following, and researching various recursive CTE methods:
WITH RCTE AS
(
SELECT Expense.Id, Expense.ParentId, Expense.ParentType, 1 AS Lvl, Expense.Id as startId FROM Expense
UNION ALL
SELECT rh.Id, rh.ParentId, rh.ParentType, Lvl+1 AS Lvl, rc.Id as startId FROM dbo.Expense rh
INNER JOIN RCTE rc ON rh.Id = rc.ParentId and rc.ParentType = 'Expense'
),
FilteredRCTE AS
(
SELECT startId, MAX(LVL) AS Lvl
FROM RCTE
GROUP BY startID
),
RecursiveData AS
(
SELECT FilteredRCTE.startId AS ExpenseId, RCTE.ParentId AS BudgetLineId
FROM FilteredRCTE
JOIN RCTE ON FilteredRCTE.startId = RCTE.startId AND FilteredRCTE.Lvl = RCTE.Lvl
)
SELECT *
FROM RecursiveData
Which did in-fact obtain all the child Expenses and their associated parent BudgetLine, but it also included the middle-tier expenses (such as item 1 in the example) and I cannot figure out how to filter those middle-tier items out.
Here is a script to create tables / insert sample data:
CREATE TABLE [dbo].[BudgetLine]
(
[Id] [int] IDENTITY(1,1) NOT NULL,
[Description] [varchar](500) NULL,
) ON [PRIMARY]
GO
INSERT INTO dbo.BudgetLine VALUES ('TEST123')
INSERT INTO dbo.BudgetLine VALUES ('OTHERTEST')
CREATE TABLE [dbo].[Expense]
(
[Id] [int] IDENTITY(1,1) NOT NULL,
[ParentId] [int] NOT NULL,
[ParentType] [varchar](100) NOT NULL,
[Description] [varchar](max) NULL,
) ON [PRIMARY]
GO
INSERT INTO dbo.Expense VALUES ('1', 'BudgetLine', 'Group of Expenses')
INSERT INTO dbo.Expense VALUES ('1', 'Expense', 'Expense # 1')
INSERT INTO dbo.Expense VALUES ('1', 'Expense', 'Expense # 2')
INSERT INTO dbo.Expense VALUES ('2', 'BudgetLine', 'Expense # 3')

Answer 1

Maybe I have oversimplified, but the following returns your desired results, by checking that there is no other expense row connected to the current row.
WITH RCTE AS
(
SELECT E.Id ExpenseId, E.ParentId, E.ParentType
FROM #Expense E
UNION ALL
SELECT RH.Id, RH.ParentId, RH.ParentType
FROM #Expense RH
INNER JOIN RCTE RC ON RH.Id = RC.ParentId AND RC.ParentType = 'Expense'
)
SELECT *
FROM RCTE R1
WHERE NOT EXISTS (
SELECT 1
FROM RCTE R2
WHERE R2.ParentId = R1.ExpenseId AND R2.ParentType = 'Expense'
);