Unlike OBS Studio, which supports closed captioning with Web Captioner, Streamlabs OBS only supports open captions, or captions that are always visible on your stream and can't be hidden by the viewer. Web Captioner is able to do this through the OBS WebSocket plugin, which is not available for Streamlabs OBS.
To set up open captioning with Streamlabs OBS, follow the steps for setting up screen capture in OBS Studio. The process is similar in both Streamlabs OBS and OBS Studio.
If you would like to see closed captioning in Streamlabs OBS, you can go to the Streamlabs website and vote on these related feature requests: