What the blue light filter shows
Worth being straight about first: a web page can only change what it draws. This warms this page and nothing else. A real blue light filter works at the display or operating system level — Night Shift on Apple devices, Night Light on Windows and Android, Redshift or f.lux elsewhere — and those are what you want if the goal is to warm everything you look at.
What this is good for is a warm field: a second monitor used as a soft light in the evening, a warm background to read against, or a way to see what a given colour temperature actually looks like before setting it system-wide.
Choosing a colour temperature
Around 6500K is daylight and is what most content is authored for. 4000K is a warm office light. 3000K is a domestic bulb and is the usual evening setting. Below 2000K is candlelight, which is dramatic and hard to read against.
The values come from a black-body approximation, so they line up with what the same number means on a light bulb or in a camera’s white balance.
What this test cannot tell you
This filters nothing outside this page. For a system-wide filter use Night Shift, Night Light, or f.lux. The evidence that blue light filtering improves sleep is also weaker than the marketing suggests — reducing overall brightness in the evening appears to matter more than shifting the colour.