@EA_Atic Thanks for replying, here's some more info:
Just to summarize:
Skins I have including a highlighted General Liu Rifle skin:
https://imgur.com/ZvSdkrY
The skins tab completely missing from the Customize soldier menu, also not correctly showing the skin I currently have selected, instead showing default only:
https://imgur.com/MKbGSj0
Some extra info showing that I have indeed unlocked every gun:
https://imgur.com/YKm12Bc
A picture of all non-Microsoft services:
https://imgur.com/YKSxkCH
The one service not showing (since the window can't be resized) is the Steam process. So basically, non MS services are Google, Steam, GOG Galaxy, Origin, Razer (mouse), AMD and PAExec (GPU driver related). I mean, I'm pretty close to clean booting by default. But yes, nothing is interfering with Origin or Battlefield 1 properly communicating. I also completely disabled the firewall to test and it did not help. I wouldn't recommend others doing this, but being that I tend to have safe internet habits, it's a non-starter for me.
Also, I attached my DXdiag, but in my troubleshooting experience of many, many years of playing PC games, I can see that this is not on my end. (I also have the MyMSInfo.txt if needed, but I'm pretty sure it won't reveal anything other than everything is running cleanly on my end.)
Likewise, Battletracker had a popup window stating that DICE has stated there is an issue with servers and some players stats are not properly updating on their site. I can't state anything with respect to the validity of this statement, but it is what it is.
I suppose it's just a waiting game until DICE sort it out. Thanks anyway.