I had the same problem, even after increasing the size of the problematic columns in the table.
tl;dr: The length of the matching columns in corresponding Table Types may also need to be increased.
In my case, the error was coming from the Data Export service in Microsoft Dynamics CRM, which allows CRM data to be synced to an SQL Server DB or Azure SQL DB.
After a lengthy investigation, I concluded that the Data Export service must be using Table-Valued Parameters:
  You can use table-valued parameters to send multiple rows of data to a Transact-SQL statement or a routine, such as a stored procedure or function, without creating a temporary table or many parameters.
As you can see in the documentation above, Table Types are used to create the data ingestion procedure:
CREATE TYPE LocationTableType AS TABLE (...);
CREATE PROCEDURE dbo.usp_InsertProductionLocation
  @TVP LocationTableType READONLY
Unfortunately, there is no way to alter a Table Type, so it has to be dropped & recreated entirely. Since my table has over 300 fields (😱), I created a query to facilitate the creation of the corresponding Table Type based on the table's columns definition (just replace [table_name] with your table's name):
SELECT 'CREATE TYPE [table_name]Type AS TABLE (' + STRING_AGG(CAST(field AS VARCHAR(max)), ',' + CHAR(10)) + ');' AS create_type
FROM (
  SELECT TOP 5000 COLUMN_NAME + ' ' + DATA_TYPE
      + IIF(CHARACTER_MAXIMUM_LENGTH IS NULL, '', CONCAT('(', IIF(CHARACTER_MAXIMUM_LENGTH = -1, 'max', CONCAT(CHARACTER_MAXIMUM_LENGTH,'')), ')'))
      + IIF(DATA_TYPE = 'decimal', CONCAT('(', NUMERIC_PRECISION, ',', NUMERIC_SCALE, ')'), '')
      AS field
  FROM INFORMATION_SCHEMA.COLUMNS
  WHERE TABLE_NAME = '[table_name]'
  ORDER BY ORDINAL_POSITION) AS T;
After updating the Table Type, the Data Export service started functioning properly once again! :)