Try quote_identifiers=False

https://docs.snowflake.com/en/developer-guide/snowpark/reference/python/1.1.0/api/snowflake.snowpark.Session.write_pandas

quote_identifiers – By default, identifiers, specifically database, schema, table and column names (from DataFrame.columns) will be quoted. If set to False, identifiers are passed on to Snowflake without quoting, i.e. identifiers will be coerced to uppercase by Snowflake.