Thanks for the feedback. Unfortunately that's just how fluid temperatures work in Factorio, it has always been a bit janky. There is only one steam fluid, called "Steam" but you can produce it at different temperatures in different ways. This is no different to vanilla Factorio, where boilers produce 165°C steam and Heat exchangers (and acid neutralization) produce 500°C steam.
I don't have the game open in front of me right now, so it might be possible to move things around in factoriopedia to improve clarity. When you say that "steam 500 C is on intermediates page", what you're actually seeing there is only a recipe, which produces 500°C steam - the recipe is called "Boil water", and I suspect if you click on the result of the recipe (steam), it will take you to the separate page for "Steam" in the fluids tab. Hopefully the "Steam" page in the fluids tab also links to "Boil water" (maybe under "Alternate recipes"?). I think I could change it so that the "Steam" page has the boil-water recipe there directly, but I'm not sure that that would help, as many players will just assume that steam can only be created from boilers/heat-exchangers and I don't want them to miss that there's a new recipe to produce steam. Maybe the "Boil water" icon should be changed from just the steam icon to an icon that represents turning water into steam? However, generally recipes with only one product just share the icon with the product.
Hopefully I've emphasised in enough places that you need 500°C steam for the Luna rocket silo, and 125°C steam is not sufficient.