WhatonEarth your wording is very impolite, please work in that. If you seek help on a forum of enthusiasts (that don't get paid anything for their effort) the least thing you can do is being nice.
That being said, let's get through your post, maybe I can help.
WhatonEarth I'm trying to install this program on a new phone that I spent $800 on and whose seal I've broken, meaning that it's $800 down the toilet if I can't figure out this mess.
You paid this to Google, not GrapheneOS. The devs get nothing unless you donate which I highly recommend if you find yourself enjoying the system. If you end up not being able to install GrapheneOS, you can make use of the shop return policy or sell it on the used market. Even if you get an error sometime during installation, it should always be possible to install the original Pixel OS (see bottom of installation manual) so you don't have an 800$ brick.
WhatonEarth I should just be able to click on various obvious places on the screen and load this program onto the device like every computer program ever until about 10 years ago
Have you tried installing an OS like Windows 11 from scratch? I find installing GrapheneOS much simpler, especially since I don't need to make a bootable USB stick in the first place. The web installation guide is pretty straightforward.
WhatonEarth I've got the phone plugged into the computer and the phone on the "bootloader" screen, and when I click the button to "Unlock bootloader", it gives the message "Error: Bootloader was not unlocked, please try again!"
Please read the installation guide, it says
Use one of the volume buttons to switch the selection to accepting it and the power button to confirm.
It's how the fastboot mode works. If you can't change the option via the volume bottoms, maybe the hardware is defect or jammed and needs to be repaired, let's hope that's not the case.
WhatonEarth After it begs me to try again, I do the polite thing and try again. And again. And again. It keeps coming up. Again and again. It keeps asking me to try again, and I keep complying again.
I understand the frustration, but repeating the same thing and expecting another result won't help you. If it's not user error and the volume keys don't work as intended, it's probably a hardware defect.
WhatonEarth Can someone please post a link that I can go to that I can just double-click on and have the damn program get loaded onto my phone? Thank you. It shouldn't be this hard. There isn't any excuse.
The web installer that you are using is already the most user friendly way I have seen when it comes to installing an OS on any device (and I have installed plenty of custom roms or Linux distributions). You won't find anything simpler, except using the Pixel with its original OS. That's the convenient route, but not private. Achieving more privacy in today's world unfortunately comes with some inconvenience, because big companies profit way too much from invading your privacy. Blame Google, Apple, Microsoft and your government for this.
We are just here to make privacy and security the most convenient possible. In my opinion GrapheneOS is excelling at that in daily usage and even the installation has been made easy.
If this is indeed too much work for you or the hardware is defect, but you still want to achieve the privacy and security of GrapheneOS, I recommend you return your Pixel 8 Pro and buy it with GrapheneOS pre-installed from a trustworthy reseller (at a premium).