Get every column in database that contains only Null records
As per my comment, the actual querying of the tables to check which nullable columns are completely NULL is the more difficult part to this problem.
To get you started you can use Dynamic SQL and the system DMVs to build the queries you'll need like this:
-- Temp table to store the results for later
DROP TABLE IF EXISTS #Results
CREATE TABLE #Results (TableName VARCHAR(1000), ColumnName VARCHAR(1000), RowsCount INT, NonNullCount INT)

-- Dynamic SQL variable to execute after we build it out recursively
DECLARE @DynamicSQL NVARCHAR(MAX) = ''

-- Uses the sys DMVs to recursively build which columns and tables to query
SELECT @DynamicSQL = @DynamicSQL + 
'
     INSERT INTO #Results
     SELECT ' + S.[name] + '.' + T.[name] + ' AS TableName, ' + C.[name] + ' AS ColumnName, COUNT(*) AS RowsCount, COUNT([' + C.[name] + ']) AS NonNullCount 
     FROM [' + S.[name] + '].[' + T.[name] + '];
'
FROM sys.Tables AS T
INNER JOIN sys.Schemas AS S
     ON T.[schema_id] = S.[schema_id]
INNER JOIN sys.Columns AS C
     ON OBJECT_ID(S.[name] + '.' + T.[name]) = C.[object_id]
WHERE C.is_nullable = 1;

-- PRINT @DynamicSQL -- Used for debugging
-- Executes the above dynamic SQL
EXEC sp_ExecuteSQL @DynamicSQL; 

-- Get the final results of which columns only contain NULLs
SELECT TableName, ColumnName
FROM #Results
WHERE RowsCount &gt; 0 -- If the RowsCount is 0 then the table is empty so can't determine if the column only contains NULLs when there's no rows to begin with (but you can remove this predicate if you want to include empty tables too)
     AND NonNullCount = 0 -- If the non null count is 0 then the column only contains NULLs
ORDER BY TableName, ColumnName

The above theoretically should answer the question. I had to type it on my phone and from memory, so if there's any minor syntactical errors, let me know and I can easily fix. You can also switch the comments around on the line that prints the dynamic SQL with the one that executes it, to help debug any syntactical issues with the dynamic SQL.