No, the MySQL solution is not standard SQL. MySQL user variables are an extension to ANSI/ISO SQL.
SQL-99 Complete, Really is a free, online resource describing the SQL specification in a human-readable manner. It's an online version, hopefully posted with permission of its authors, of the book by the same name.
However, I don't know of a similar resource for SQL:2003 or later. You'd have to purchase the specification documents from ISO. They are not inexpensive, and they are dry reading.
IMHO, trying to limit yourself to SQL that is 100% portable and compliant with the abstraction of the language is too constraining. For example, try to find a single SQL data type that is implemented exactly the same in all brands of RDBMS, and exactly matching the language specification. I haven't found one.