If you need push data from Power Query part of Power BI in to table, best way is reuse Power Query script in Power Query Source for SSIS. If you need push whole Power BI DataModel (which is builtin SSAS Tabular database), it is not possible push to MSSQL relational database. But in some cases is possible convert to regular SSAS Tabular database.
"Power BI Shared Dataset" = tabular cube = data model definition + data (stored in SSAS tabular database). It may consist of multiple tables, relations, hierarchies, calculations, and so on. There no any output or export for whole model. There nothing what is able load to MSSQL relational table. But if you mean: 1) output of specific table which is loaded in to model -> yes, each table is filled by PQ, and you can use Power Query Source for SSIS to load also to MSSQL DB
2) output of DAX/MDX query executed on PBI data set -> yes, output of DAX query is table and you can load to MSSQL DB (e.g. using SSIS OLEDB connection, but there is more ways)
3) output of binary copy of whole tabular database (BIM file) -> it is not supported, and there is no strong reason for it, but technically it is possible, you can make copy and backup database and load to MSSQL as blob
If I understand your note, you probably mean point 2)