Interesting, so you're saying that that OS-level time preference is available via JavaScript? I wasn't able to figure out how to query that in a little bit of trying, so I assumed there was no API for it.
If there actually is, I'm now even more upset at that log web UI.
For me, the first returns 24 hour time and the second returns 12 hour time. Because 12 hour time is default for my primary locale (en-AU), but I override it to 24 hour time in my macOS settings.
I know the same works on Windows, and I’m sure it works on Linux too, just the way you configure it is different for each OS.
If there actually is, I'm now even more upset at that log web UI.