After asking on the Blade & Sorcery Discord and using Pickysaurus's information provided, a helper on the Discord page named Alex managed to figure it out.
Just as Pickysaurus explained, the mods were improperly nested inside of other folders. Here is an example of a regular mod:
StreamingAssets > Mod Name Folder 1 > manifest.json
As for the mods that were inoperable:
StreamingAssets > Mod Name Folder 1 > Mod Name Folder 2 > manifest.json
The game reads Mod Folder 1. If it doesn't have manifest.json in it, the mod will not appear. The same goes for Vortex and the load order mechanic.
Additionally, I also made a mistake in my previous post in which I attempted a manual install. I messed up because I extracted Mod Folder 1 into StreamingAssets instead of Mod Folder 2. As an additional note, Mod Folder 2 might be a lot of folders depending on how the mod is organized (e.g. each Mod Folder 2 is its own weapon folder and each has its own manifest.json). To manually extract them into StreamingAssets, make sure you copy each Mod Folder 2 into StreamingAssets, NOT Mod Folder 1.
I'm going to contact every Mod Author who has packaged their mods with both Mod Folder 1 and Mod Folder 2 and inform them that the game isn't able to properly read the way it's formatted. Hopefully they can put all of the contents of Mod Folder 2 into #1 to solve the issue.
Thank you for the help Pickysaurus. Hopefully this helps anyone else who's experienced the problem.
