Answering my on question here. I finally got an answer to a question I posted on the Server Fault stack overflow site: How do you check/start SQL browser service under linux?
The answer is simplicity in itself. You don’t - because the SQL browser service isn’t supported under Linux!
This can be seen in the documentation from MS for MS-SQL 2019 Unsupported features & services
Protip: Read all of the documentation for a product in order to avoid asking stuuuupid questions!