There is ALWAYS SOME latency (delay) through the computer (related to buffers and the multitasking operating system, which is ALWAYS multitasking.) Sometimes latency can be brought-down to where it’s unnoticeable, and sometimes not.
Audacity does support SOME real-time effects. I’m not sure if they work for monitoring.
Audacity is intended as an audio file editor/processor that can also record, and of course any audio editor has to play.
DAW applications can use real-time effects in the monitoring path. DAWs are also intended for file recording/mixing/processing, but some people do use them “live”. DAWs also support ASIO drivers, which are designed for low-latency, but you also need hardware that supports ASIO.