I came across the Phoenixdex website while researching for my own fan-region. I'm curious as to how you build the website to display your works, and do you have any recommendations when it comes to website-building?
The Phoenixdex website is custom-coded, built on top of the ProcessWire PHP framework. ProcessWire and frameworks like it are great for building full-on database applications, but a project of that scope is usually way beyond what most people are interested in when they just want an easy personal website for showing off their fakemon stuff. I only bothered building all that myself because I work with web design and development as my actual job and it's a hobby I've had for a long time, so it used a skillset I happened to have already.
You can always go the same route if you either have or want to learn the same skills, but if you're not yet familiar with coding for the web, be aware that you'll need to obtain hosting for your site, and to learn about databases and the programming language/frameworks of your choice. (If you are curious about this, let me know and I can share some resources to help you get started/see if it's something you're really interested in!)
The much, much easier route is to sidestep all that and create a wiki-style site for your project. This is what I did before I created the fully-custom site, actually! (Although I still used my own hosting and made a few modifications, because again that is adjacent to my job/hobby and also I am a nerd.) This gives you a website that's nice and searchable but is also much easier to put together pages for than needing to learn full HTML or some kind of templating language and database APIs or whatever. It would basically be making your own custom Bulbapedia.
Most people used to recommend Fandom/Wikia for this, but there are a lot of awkward limitations and obnoxious ads and policies and it's probably best to stay away from all that. It looks like Miraheze ( https://miraheze.org/ ) is the big not-crappy wiki farm these days. I haven't used them myself so I don't have any personal experience to share about Miraheze as a host, but as I understand it they run a pretty straightforward version of MediaWiki (the same software created for Wikipedia and used for sites like Bulbapedia) so there are plenty of guides and resources out there for learning to use and customize it without Fandom's janky corporate nonsense confusing things. It's even possible to lay things out in the same format Bulbapedia uses, if you're interested in that and up for learning a little bit about MediaWiki templates, but that's far from necessary—you can just put your fakemon info, or trainer or move or whatever you're making a page for, onto the page in whatever format's easiest for you.
You can see an example of a fangame wiki made using Miraheze + MediaWiki on Pokémon Flux's wiki here: https://pkmnflux.miraheze.org/wiki/Main_Page They've opted to use a Bulbapedia-like layout for their content as well.
Sorry for the super basic yet kinda lengthy overview, but there're a lot of weeds you can get into when talking about website creation. I hope it at least helps get you pointed toward something that'll work for you! Let me know if anything was unclear, and best of luck getting your fan region site set up!