> this old timey way of using computers, where you had a general purpose machine that was personal that you programmed to do things you needed,

Personal machines are actually new-time'y, not old-time'y. In the old times there weren't that many computers, and you accessed one via a terminal.

The difference is more in how remote services are now things you can't program and modify and tinker with, but rather closed-source "products" or "services" in shiny wrappers.