Regarding Twitch: They probably assume it's your internet connection that's to blame, not specific devices, but if you can watch YouTube without issues then clearly it's something network related located between you, Twitch and whoever is streaming to Twitch that's at fault. That, uh, is how Twitch works, right? Someone streams to it live, and then Twitch broadcasts that to whoever is watching? Depending on how Twitch broadcasts the streams it's possible that your ISP is throttling the connection. Live streams are usually served using a different format and sometimes even different protocol to how videos on YouTube are served, but I'm less sure that it could be reliably detected and throttled over a secure connection. I can only guess that Twitch uses secure connections.
Anyway, for the past few months I've felt a gradual but steady decline in my motivation, energy and drive to do anything that wasn't mandatory. That seems to have gotten noticeably worse over just the past few weeks to the point that even semi-mandatory things are starting to feel optional, and it's starting to bother and worry me. It feels like burnout, but remarkably, taking time off twice in the past three months has not helped. That strongly implies that work isn't the problem, which I already suspected was the case since my job is pretty relaxed.
That leaves everything else in my personal life for me to consider, and nothing really jumps out at me as being particularly stressful or draining. Yet, here I am feeling completely and thoroughly mentally fatigued, so it must be some combination of things.
Hopefully this is just a temporary feeling, but I know from related experience that this kind of thing tends to get worse on its own and not better.