It looks to me like just updating the columns to `NULL` will release pages for reuse. Here's a Very Scottish® demo, to celebrate it being almost 5PM, EST.

    USE tempdb;
    
    DROP TABLE IF EXISTS dbo.RobertBurns;
    
    CREATE TABLE dbo.RobertBurns
    (
        Id INT IDENTITY(1, 1) PRIMARY KEY CLUSTERED,
        Scotch VARCHAR(50),
        HaggisAddress VARBINARY(MAX)
    );
    
    DECLARE @AddressToAVarbinaryHaggis VARBINARY(MAX); 
    DECLARE @AddressToAHaggis NVARCHAR(MAX) = N'
    Good luck to you and your honest, plump face,
    Great chieftain of the pudding race!
    Above them all you take your place,
            gut, stomach-lining, or intestine,
    You''re well worth a grace
            as long as my arm.
    
    The overloaded serving tray there you fill,
    Your buttocks shaped like a distant hilltop,
    Your wooden skewer could be used to fix a mill
             if need be,
    While through your pores your juices drip
             like liquid gold.
    
    His knife see the serving-man clean,
    And then cut you up with great skill,
    Making a trench in your bright, gushing guts
            To form a ditch,
    And then, 0h! What a glorious sight!
            Warm, steaming, and rich!
    
    Then, spoonful after spoonful, they eagerly eat,
    The devil will get the last bit, on they go,
    Until all their well-stretched stomachs, by-and-by,
            are bent like drums,
    Then the head of the family, about to burst,
            murmurs “Thank the Lord".
    
    Is there a pretentious soul who, over his French ragout,
    Or Italian cuisine that would make a pig sick,
    Or French stew that would make that same pig ill
            with complete and utter disgust,
    Looks down with a sneering, scornful attitude,
            on such a meal? (as Haggis)
    
    Poor devil! See him over his trash!
    As feeble as a withered bullrush,
    His skinny leg no thicker than a thin rope,
            His fist the size of a nut,
    Through a river or field to travel,
            Completely unfit!
    
    But look at the healthy, Haggis-fed person!
    The trembling earth respects him as a man!
    Put a knife in his fist,
            He''ll make it work!
    And legs, and arms, and heads will come off,
            Like the tops of thistle.
    
    You Powers who look after mankind,
    And dish out his bill of fare,
    Old Scotland wants no watery, wimpy stuff
            That splashes about in little wooden bowls!
    But, if You will grant her a grateful prayer,
            Give her a Haggis!';
    
    
    INSERT dbo.RobertBurns (Scotch, HaggisAddress )
    SELECT TOP 1000 
    CASE WHEN x.c % 15 = 0 THEN 'Laphroaig'
    	 WHEN x.c % 5 = 0 THEN 'Lagavulin'
    	 WHEN x.c % 3 = 0 THEN 'Port Ellen'
    	 ELSE 'Ardbeg'
    END AS Scotch, 
    CONVERT(VARBINARY(MAX), REPLICATE(@AddressToAHaggis, x.c % 20 + 1))
    FROM (
    SELECT ROW_NUMBER() OVER (ORDER BY @@ROWCOUNT) AS c
    FROM sys.messages AS m
    ) AS x;
    
    CREATE INDEX ix_novarbinary	ON	dbo.RobertBurns (Scotch, Id);
    CREATE INDEX ix_yesvarbinary ON	dbo.RobertBurns (Scotch, Id) INCLUDE (HaggisAddress);
    

With rows inserted, let's check on our index pages.

    SELECT   OBJECT_NAME(i.object_id) AS table_name,
             i.name AS index_name,
             MAX(a.used_pages) AS leaf_me_alone
    FROM     sys.indexes AS i
    JOIN     sys.partitions AS p
    ON p.object_id = i.object_id
       AND p.index_id = i.index_id
    JOIN     sys.allocation_units AS a
    ON a.container_id = p.partition_id
    WHERE OBJECT_NAME(i.object_id) = 'RobertBurns'
    GROUP BY i.object_id, i.index_id, i.name
    ORDER BY OBJECT_NAME(i.object_id), i.index_id;
    

After the insert, I get this. Actual pages may vary for you.

    table_name	index_name	                    leaf_me_alone
    RobertBurns	PK__RobertBu__3214EC074BE633A2	5587
    RobertBurns	ix_novarbinary	                10
    RobertBurns	ix_yesvarbinary	                5581

Let's `NULL` out some rows!

    UPDATE rb
    	SET rb.HaggisAddress = NULL
    FROM dbo.RobertBurns AS rb
    WHERE rb.Id % 15 = 0;

And check back in on our pages:
    

    table_name	index_name	                    leaf_me_alone
    RobertBurns	PK__RobertBu__3214EC074BE633A2	5300
    RobertBurns	ix_novarbinary	                10
    RobertBurns	ix_yesvarbinary	                5273

    
So page count was reduced. Huzzah! For the two indexes that touch our `VARBINARY` data, they lost a buncha pages. That means they're back in circulation for other objects to use. Since I'm in tempdb, they probably get gobbled up pretty quickly by all the garbage things that go on here.

Now let's put some data back in:

    INSERT dbo.RobertBurns (Scotch, HaggisAddress )
    SELECT TOP 10 rb.Scotch, rb.HaggisAddress
    FROM dbo.RobertBurns AS rb;

And checking back in:

    table_name	index_name	                    leaf_me_alone
    RobertBurns	PK__RobertBu__3214EC074BE633A2	5330
    RobertBurns	ix_novarbinary	                11
    RobertBurns	ix_yesvarbinary	                5305

Page counts inched up a bit.

So, looks like you don't have to do anything too crazy, or even shrink your database to get space reuse. I think you were conflating the behavior of dropping columns and needing to run `DBCC CLEANTABLE` with what you're actually doing.

Hope this helps!