But is it normal to see 50yo’s still programming?

It's never been very rare. But, it's about to be a lot more normal, since the dot com boom was about 25 years ago now. College graduate age people who got sucked into the game then are in their late 40's.

Or is everyone expected to “move up” at some point and not be a programmer forever.

No, I think of programming as engineering, and the trope of the wise old engineer is a trope I'd like to embody some day. Real engineers engineer 'til they die. Managing engineering projects is not engineering. There's simply too much process, and separation from where the rubber meets the road, to ever think a single real engineering thought.

Plus, the programming world needs sage developers. Especially nowadays, and especially in webdev. That field is getting chock full of devs with no real deep fundamental understanding of the web. If all the old webdevs suddenly quit, webdev as we know it would spiral into insanity. It's barely clinging to sanity as it is.