There’s no “hacker culture.” The movies are fantasies. Programmers in cubicle farms and at standing desks in home offices writing code for money are not a culture. A side project isn’t hacking. The people who do what used to be called hacking are criminals.
The definitions of “hacker” offered by Richard Stallman and Eric Raymond — two people devoid of what we usually mean by “culture” — use the term to describe curiosity, fun, and inventiveness, which English already has good words for.
I'm old enough to remember when hackers were unhappy about the rising usage of your definition of "hacker", a pop-culture misunderstanding which did not rise from hacker culture itself...
When I started, around 1982-4, (in my world) the word meant, someone who knows arcane stuff about a computer hardly anyone knows, and with that can do what seems magic. Usually, someone whose knowledge of the hardware means they can do magic with programming. I think I didn't hear the grey/black hat sense (or the hardware-hacking sense or the "life hack" sense of "hack") until years later.
p.s. And mostly, computers weren't connected to anything else. I don't mean magic on a network or anything, just on your own computer.
There is and was multiple meanings to the word. I can count at least 3 (in chronological order):
1. Open source hackers/hardcore systems programmers that culturally originated in MIT back in 60s (Tech Model Railroad Club, Free Software Foundation, Linux, Free/Open/Net BSD, GNU).
2. Security hackers.
2a. Blackhats: cyber criminals, radical take-no-prisoners hacktivists (90s Phrack, to some extent Defcon, LulzSec, hatefag faction of Anonymous).
2b. Whitehats: security engineers working in corporate settings (both on offensive and defensive sides of security), security consultants, bug bounty hunters (to some extents Defcon, Blackhat conference, NullCon, bug bounty platform communities (HackerOne, BugCrowd, Intigriti)).
2c. Grayhats: some combination/midpoint between the whitehats and blackhats.
The definitions of “hacker” offered by Richard Stallman and Eric Raymond — two people devoid of what we usually mean by “culture” — use the term to describe curiosity, fun, and inventiveness, which English already has good words for.