PostgreSQL doesn't control execution of its child processes explicitly. If I borrow your words, PostgreSQL delegates that task to the OS.
PostgreSQL allows multiple clients to connect simultaneously. Each client connects a child process (referred to as a
backend process), and each running backend process handles all queries issued by the connected client. It is a very simple and classical server-client type multi-process architecture.
(I add more information.)
PostgreSQL can control the maximum number of connected clients by the configuration parameter
max_connections (in the same way as MySQL),
but does not control the activities of the running backend processes depending on the server activity.
In addition, some helper processes, such as autovacuum related processes and checkpointer, can be controlled their activities by themselves depending on the server activity.