As Bitwarden states in the core readme (https://github.com/bitwarden/core#requirements) "These dependencies are free to use." And if you lookup the licensing on MSFTs website (https://www.microsoft.com/en-us/sql-server/sql-server-2017-p...) you can see that the SQL Server Express version is free.
Note: No, I'm not an MSFT employee and not related in any way to the mentioned company. I'm just a (not so regular) human being who first looks up information before posting statements.