Cursors can be replaced by while loops to get that functionality: https://learn.microsoft.com/en-us/azure/synapse-analytics/sql-data-warehouse/sql-data-warehouse-develop-loops
In the case of FOR XML, the Synapse-compatible equivalent is going to be STRING_AGG(): https://learn.microsoft.com/en-us/sql/t-sql/functions/string-agg-transact-sql?view=azure-sqldw-latest
There are a couple things in the SQL language reference to help you find out whether a given command is available on your SQL version- first is by explicitly setting the docs to Synapse, and the second is to look at the supported versions in the header.