MySQL 8.0

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CREATE TABLE test (id INT);
SHOW CREATE TABLE test;

Table
Create Table

test
CREATE TABLE `test` (
  `id` int DEFAULT NULL
) ENGINE=InnoDB DEFAULT CHARSET=utf8mb4 COLLATE=utf8mb4_0900_ai_ci

SET @sql := CONCAT ( 'ALTER TABLE test ',
                     'MODIFY COLUMN id INT ',
                     'COMMENT \'saved at ' , CURRENT_TIMESTAMP, '\'' );
SELECT @sql;

@sql

ALTER TABLE test MODIFY COLUMN id INT COMMENT 'saved at 2023-03-10 13:32:32'

PREPARE stmt FROM @sql;
EXECUTE stmt;
DROP PREPARE stmt;

Statement prepared

Records: 0  Duplicates: 0  Warnings: 0

SHOW CREATE TABLE test;

Table
Create Table

test
CREATE TABLE `test` (
  `id` int DEFAULT NULL COMMENT 'saved at 2023-03-10 13:32:32'
) ENGINE=InnoDB DEFAULT CHARSET=utf8mb4 COLLATE=utf8mb4_0900_ai_ci