I cooked dinner, but I'm not a chef.
I fixed my car, but I'm not a mechanic.
I took people fishing, but I'm not a charter guide.
I remodeled my house, but I'm not a contractor.
I stopped the leak, but I'm not a plumber.
So, what makes you think if I wrote a story or novel, I would consider myself a writer?
All of the things you mentioned are basic applications of skillsets anyone can do with a little instruction. Except the contractor and charter fisherman thing, and the titles of both of those things imply money exchanging hands. If you write reports for work are you a writer? Probably not. But if your purpose at work is to produce words and that's it, not as representation of other work you do, but you were hired because of your facility with words, you'd be a writer. Because at that point, chances are you have chosen to devote a certain amount of energy to writing and the craft. And that's where the good-faith claim of "being" something comes from, knowing that you have devoted a certain amount of yourself to "being" that thing.
I can change my oil, but I'm not a mechanic. If I devoted time and energy to learning about cars, souping them up, fixing them up, and generally became a gear-head, I might say I was a mechanic even if I wasn't professionally.
In my opinion, it comes down to the motivation behind it. I would wager that every professional writer at one point or another was writing things they did not have to. Maybe now they only write for their professional lives, but at some point they had to develop the craft and that desire and that drive is what I think makes someone a writer. A reporter probably wrote for the school paper when they didn't have to. An academic writer pursued degrees that they did not have to and wrote thesises which the rest of us won't have to. Novelists spent hundreds of hours polishing work, never knowing if it would see the top of a slush pile.
If you write a novel, are you a writer? Hell yeah. Even if the novel is horrible, it still took you a substantial amount of energy to complete it. Energy and self-drive. You're not a good writer. You're not a paid writer. But you're a writer.
For all of your examples, most of them were the name of professions. We have names for professional writers. Reporters, copywriters, etc etc. But to just be a writer, I think that's like calling oneself a musician or an artist. I never would, in polite company, but I feel you have the right to if you identify yourself with the craft.