I found the Twitch Launcher logs complaining about the HTTP 403 forbidden status error, however, the Minecraft Launcher acted differently when trying to recreate the logs and didn't even attempt to download the libraries. Previously, it ran into the same HTTP 403 status error on the same file.
Twitch Log: https://pastebin.com/p1RJZ9UW
Minecraft Log: https://pastebin.com/hs7wQR7k
PS: I've seen SSL failures before using the Minecraft Launcher's built-in Java runtime to manually install forge instead of a system Java installation. I'll post a forge install log if I se