Add Column with Default value from existing JSON Column

You would need to surround the expression given as a default with parentheses for MySQL to properly understand it:

alter table gdn_audit_trail 
    add column solution_id varchar(50) 
    default (json_unquote(json_extract(details,'$.SolutionID'))) after action_type; 
         -- ^ --                                            -- ^ --

Note that using expresions in the DEFAULT clause requires MySQL 8.0.13. In earlier versions, only literal constants were allowed (with current_timestamp being the only exceptions). This is well explained in the documentation:

Handling of Explicit Defaults as of MySQL 8.0.13

The default value specified in a DEFAULT clause can be a literal constant or an expression. With one exception, enclose expression default values within parentheses to distinguish them from literal constant default values.

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Handling of Explicit Defaults Prior to MySQL 8.0.13

With one exception, the default value specified in a DEFAULT clause must be a literal constant; it cannot be a function or an expression.