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I have a multi-tenant database where I am utilizing an AccountId column within all tables as a part of the composite Primary Key for tenant isolation. Is it beneficial to create additional non-clustered indexes on each column that is part of the composite Primary Key to assist SQL Server with maintaining accurate statistics and improving query performance when joining to lookup tables?

For instance, within an associative table that defines one-to-many relationships between an Account and the American State in which they have offices, in theory which of the two options is preferable given the following structure and sample query?

Create the Account and State tables and populate with sample data.

DROP TABLE IF EXISTS [dbo].[Account];

DROP TABLE IF EXISTS [dbo].[State];



-- [Account] table and sample values.

IF OBJECT_ID('[dbo].[Account]', 'U') IS NULL

BEGIN

    CREATE TABLE [dbo].[Account] (

        [AccountId] [int] IDENTITY(1,1) NOT NULL

        ,[AccountAlias] [varchar](3) NOT NULL

        ,[AccountName] [varchar](128) NOT NULL

        ,CONSTRAINT [PK_Account] PRIMARY KEY CLUSTERED ([AccountId] ASC)

        ,CONSTRAINT [UQ_Account_Alias] UNIQUE NONCLUSTERED ([AccountAlias] ASC)

        ,CONSTRAINT [UQ_Account_Name] UNIQUE NONCLUSTERED ([AccountName] ASC)

    );



    SET IDENTITY_INSERT [dbo].[Account] ON;



    INSERT INTO [dbo].[Account] ([AccountId], [AccountAlias], [AccountName])

    VALUES (1, 'SA1', 'Sample Account 1'), (2, 'SA2', 'Sample Account 2'), (3, 'SA3', 'Sample Account 3')



    SET IDENTITY_INSERT [dbo].[Account] OFF;

END;

GO



-- [State] table and sample values.

IF OBJECT_ID('[dbo].[State]', 'U') IS NULL

BEGIN

    CREATE TABLE [dbo].[State] (

        [StateId] [tinyint] IDENTITY(1,1) NOT NULL

        ,[StateCode] [varchar](2) NOT NULL

        ,[StateName] [varchar](32) NOT NULL

        ,CONSTRAINT [PK_State] PRIMARY KEY CLUSTERED ([StateId] ASC)

        ,CONSTRAINT [UQ_State_Code] UNIQUE NONCLUSTERED ([StateCode] ASC)

        ,CONSTRAINT [UQ_State_Name] UNIQUE NONCLUSTERED ([StateName] ASC)

    );



    SET IDENTITY_INSERT [dbo].[State] ON;



    INSERT INTO [dbo].[State] ([StateId], [StateCode], [StateName])

    VALUES (1, 'AL', 'Alabama'), (2, 'AK', 'Alaska'), (3, 'AZ', 'Arizona'), (4, 'AR', 'Arkansas'), (5, 'CA', 'California')



    SET IDENTITY_INSERT [dbo].[State] OFF;

END;

GO

Create AccountState OPTION 1 - composite Primary Key only

DROP TABLE IF EXISTS [dbo].[AccountState];



IF OBJECT_ID('[dbo].[AccountState]', 'U') IS NULL

BEGIN

    CREATE TABLE [dbo].[AccountState] (

        [AccountId] [int] NOT NULL

        ,[StateId] [tinyint] NOT NULL

        ,CONSTRAINT [PK_AccountState] PRIMARY KEY CLUSTERED ([AccountId] ASC, [StateId] ASC)

        ,CONSTRAINT [FK_AccountState_Account] FOREIGN KEY ([AccountId]) REFERENCES [dbo].[Account]([AccountId])

        ,CONSTRAINT [FK_AccountState_State] FOREIGN KEY ([StateId]) REFERENCES [dbo].[State]([StateId])

    );



    INSERT INTO [dbo].[AccountState] ([AccountId], [StateId])

    SELECT A.[AccountId], S.[StateId]

    FROM [dbo].[Account] A CROSS JOIN [dbo].[State] S

    WHERE A.[AccountId] = 1 AND S.[StateId] IN (1, 2, 3)

    UNION

    SELECT A.[AccountId], S.[StateId]

    FROM [dbo].[Account] A CROSS JOIN [dbo].[State] S

    WHERE A.[AccountId] = 2 AND S.[StateId] IN (3, 4, 5)

    UNION

    SELECT A.[AccountId], S.[StateId]

    FROM [dbo].[Account] A CROSS JOIN [dbo].[State] S

    WHERE A.[AccountId] = 3 AND S.[StateId] IN (1, 3, 5)

END;

GO

Create AccountState OPTION 2 - composite Primary Key + non-clustered indexes

DROP TABLE IF EXISTS [dbo].[AccountState];



IF OBJECT_ID('[dbo].[AccountState]', 'U') IS NULL

BEGIN

    CREATE TABLE [dbo].[AccountState] (

        [AccountId] [int] NOT NULL

        ,[StateId] [tinyint] NOT NULL

        ,CONSTRAINT [PK_AccountState] PRIMARY KEY CLUSTERED ([AccountId] ASC, [StateId] ASC)

        ,CONSTRAINT [FK_AccountState_Account] FOREIGN KEY ([AccountId]) REFERENCES [dbo].[Account]([AccountId])

        ,CONSTRAINT [FK_AccountState_State] FOREIGN KEY ([StateId]) REFERENCES [dbo].[State]([StateId])

        ,INDEX [IX_AccountState_Account] NONCLUSTERED ([AccountId])

        ,INDEX [IX_AccountState_State] NONCLUSTERED ([StateId])

    );



    INSERT INTO [dbo].[AccountState] ([AccountId], [StateId])

    SELECT A.[AccountId], S.[StateId]

    FROM [dbo].[Account] A CROSS JOIN [dbo].[State] S

    WHERE A.[AccountId] = 1 AND S.[StateId] IN (1, 2, 3)

    UNION

    SELECT A.[AccountId], S.[StateId]

    FROM [dbo].[Account] A CROSS JOIN [dbo].[State] S

    WHERE A.[AccountId] = 2 AND S.[StateId] IN (3, 4, 5)

    UNION

    SELECT A.[AccountId], S.[StateId]

    FROM [dbo].[Account] A CROSS JOIN [dbo].[State] S

    WHERE A.[AccountId] = 3 AND S.[StateId] IN (1, 3, 5)

END;

GO

Sample query

SELECT

    A.[AccountName]

    ,S.[StateName]

FROM

    [dbo].[AccountState] A_S

    JOIN [dbo].[Account] A

        ON A_S.[AccountId] = A.[AccountId]

    JOIN [dbo].[State] S

        ON A_S.[StateId] = S.[StateId]

WHERE

    S.[StateCode] = 'CA'

Of the two options, what type of index combination would be seen as most suitable to scale? Composite primary key only or composite primary key plus additional non-clustered indexes? Or is there another option that is more viable?