I've only ever come across a few companies, ever, with a solid and dedicated management track that's 100% technical. They were huge grist mills, but they at least knew not to stifle their talent.

Pretty much every small company I've ever encountered just forces technical people into management where they either atrophy or leave to stay technical elsewhere.

When HR suggests you need to "take on more responsibility" to progress, you know the writing is on the wall.