Come on, there isn't even a button "install" on the sailfish website. You certainly have to go through the "developers" menu, but even there, it's not clear where to go to install it.
If you could click one button on a website and override your entire OS, malware makers would have a field day with it.
Such things sound cool but are untenable in the real world. Microsoft used to have downloadable binaries on websites (ActiveX) and that showed what a stupid idea it was :) There's a reason internet explorer has such a bad name.
You have to grant webUSB permission and enable OEM unlocking on your Pixel, but GrapheneOS can be installed from a website: https://grapheneos.org/install/web
It is arguably easier than installing windows on a laptop (if you were someone who had done neither before), since it is just a few buttons to press.
I think you're the one with unrealistic expectations here. There's quite literally no way for you to install another OS with one click; even if you do have a device that allows you to flash other OSes to it, you have to unlock the bootloader and -- oops! That's your one click.
OP means it figuratively. Amazon's "one click" checkout isn't actually just one click, it's a metaphor for how simple they're going to make it for you to buy the item. Similarly, a "one click" install of another OS should be taken to mean "dead simple to install" instead. You're welcome to debate how easy it is to install Sailfish OS on those grounds, but if we're being pedantic then there's quite literally no solutions that actually fit the parent's description.
https://sailfishos.org/