A Pi-hole can absolutely be a contributing factor. It comes under the general heading of Check for VPN or other security software in If Safari doesn't open a page or work as expected on Mac which is the reason I emphasize the need to follow all of its suggestions even if they appear to be trivial or inapplicable.
Excerpted from its documentation,
"The Pi-hole® is a DNS sinkhole that protects your devices from unwanted content, without installing any client-side software."
That is precisely the reason Apple incorporates this passage in their suggestions:
"If you installed VPN or other software that monitors or interacts with your network connections, that software could affect your use of the website or the internet. Learn about network issues related to VPN and other software."
That passage is all-encompassing and broad in its implications, but I respectfully suggest you reconsider the comment "I have tried every suggestion in that link, every-single-suggestion." when you have not.
Aside... I do not dispute the fact a Pi-hole is a certainly a brilliant and well-executed concept. The problem with troubleshooting this site (Apple Support Communities) is that it incorporates a number of unique and proprietary features designed to protect it from exploitation and abuse. A few years ago those exploits began accelerating at a rapid pace, and many changes were implemented to address them. You know something is happening when you encounter the "We'll be right back" annoyance.
Similar challenges have no sign of abating even today — I'm specifically referring to AI-generated "chatbot" replies and questions that have the potential to overwhelm this site, rendering it useless to everyone but robots.
ASC is orders of magnitude greater than similar support forums or websites in that regard, and it is decades ahead of them in its defenses. Our Community Managers are tight-lipped about them to an almost ridiculous extreme, and if you were to contact Apple Support they are certain to be completely in the dark about them.
That's the reason you need to simplify things on the client end as much as possible. I'd start with the Pi-hole because investigating various and sundry Safari-specific settings on the Mac is certain to be even more time-consuming.
Or, just reserve Firefox for the exclusive use of this particular website. It may be the most expedient solution. I would be as reluctant to remove the Pi-hole as you are likely to be.