Are pc servers cross platform
Well, yes and no. Are there "cross platform" servers on computer? Yes. But SUPER limited, and no mod support. And only if you have a Wndows 10 copy of ARK to play on a Xbox Live server.
ARK has 7 versions of server platform, and there's 4 version of ARK that run on a computer. Here's a list with some factoids:
Xbox Live (Works with Windows10 Store) Windows10 Store (Works with Xbox Live)
*These are the servers that generally get updated first upon a deployment, but they don't get patches "often". To commercially run a Windows10 / Xbox Live server, a server host has to have the equivalent of an Xbox One per server, a commercial license of Windows10 with a valid Corporate Xbox Live account. Again, that's per server. So $200-ish for the Xbox, $15 a month for the license, $10 a month for Xbox Live, and $60 for ARK on the Xbox Live account.. It's one of the reasons why most Xbox compatible servers cost at least $40--$50 a month to rent, because it requires $285 USD upfront from the host provider to start a server for 1 month. That means that host won't see ANY profit from the server for around the first 9 months.
See the exact same notes for PS4 servers, but there's no requirement for a Windows License. Instead you have to have a Sony Playstation Server box. (Not cheap, I found one used for around $1800 once.) But unlike the windows server, you can VM instances of the server afterwards. However, each VM instance needs to have their own PS Live account for connectivity. Unlike MSoft though, Sony's corporate license allows for bulk slot participation. The cheapest data I've found indicates that with 100 licenses at a yearly rate, you can save over 50% on the cost, running about $500 a year for a sony server license to hit across multiple vmware instances. Again, it's why you find rates a bit more expensive for PS4 than for windows.
Nintendo Switch No one knows about switch pricing, but if it's going to be anything like minecraft, you're better off finding a different platform to self host on.
Steam for Windows (Cross compatable with Steam for Linux and Steam for Mac)
Steam for Winodws server is available for free. To run a steam for windows server you just need a computer with about a 2.4 ghz processor and around 8 gig of ram to self host some minor mods and about 6 people with no issues, allows for multiple copies running on VMWare without licensing costs, and in general after machine and bandwidth cost is pure profit. The average ARK Server run this way costs a host around $0.20 a "slot." or about $12.00 for a 60 slot server. When you consider power consumption it can be a bit closer to $13, and then if you consider the tech support here get paid for their work on some form of salary, you can see why the servers here can't really go lower than their pricing.
Ios / Android - Garbage in, garbage out. Game is Freemium / Pay to Win. No chance of getting to control any of that privately.
Steam for Linux (See notes for Steam for Windows) Steam for Mac (See notes for Steam for Windows)