"How do I keep up with it all? ...and even if I do, how do I know it's not obsolete in 6 months, or in the case of JS, next week?"
Most tech changes are slight variations of patterns and building blocks that you already have in your arsenal, they just look different. Maybe they simply embrace a different syntax or call a pattern by a different name, but often times they’re based on the same foundational software development blueprints you use on your current tech stack of choice.
Instead of worrying about how to learn it all and ultimately feel like you need to learn everything, embrace the technology wave with the knowledge that you’ve probably seen the new shiny dog in the window or something very similar. Fall back on your core development skill set as you jump into new techs and love the fact that you as a technologist are paired with an exciting and ever evolving world.