The SQL Server Team has announced SQL Operations Studio:
We are excited to announce that SQL Operations Studio is now available in preview. SQL Operations Studio is a free, light-weight tool for modern database development and operations for SQL Server on Windows, Linux and Docker, Azure SQL Database and Azure SQL Data Warehouse on Windows, Mac or Linux machines.
Download SQL Operations Studio to get started.
It’s not SSMS, but it is cross-platform. And I think that over time, it will end up being better than SSMS.