How can I update my Safari browser on my Mac laptop using the High Sierra OS?

Safari generally gets updates only at the release of a new operating system, but occasionally is updated for recent old systems near the release of a new macOS. If memory serves, the last release of Safari for High Sierra was version 13 late in 2019, which was a year or so after High Sierra was superceded by Mojave.

I can't find it on Apple's website. Either it remains available via your Software Update or it has been retired. Or perhaps this is the version you have installed.