My (35M) gf (31F) is intolerant of mistakes, makes me swear to try harder

My (35M) girlfriend (31F) and I are a new couple, less than a year old. We still have a lot to learn about each other, but we're mature, independently successful, and we have chemistry. So we've been living together for 3 months.
Over time, she's become so critical of me that I'm scared to make mistakes. If we're walking through town and I take a second to notice the "Walk" sign is green, she hounds me for not paying attention. If I forget a detail about something that happened at her job, even if I recall moments later, she'll ask why I didn't remember faster. If I press the wrong setting on the water purifier and the cup overflows, even if I clean it up and say I'm sorry, she won't let it go.
By "won't let it go," I don't mean she needs time to get over it. I mean she keeps a written log of my failures. She says they're important because she needs a dependable man in order to plan a secure future. Mistakes show a lack of dependability, forcing her to question if I'm right for her. She often says, "If I can't rely on you to make the right choice with little things, how can I rely on you to make the right choice with big things?"
She considers some mistakes forgivable, as long as I promise to try harder next time, and never dispute my error. If I suggest that a small mistake isn't a big deal, she regards this as irresponsible and unaccountable. And no mistake is exempt from being recorded in her journal, forgiven or not.
This scrutiny pervades every aspect of our lives. Two weeks ago, we were lying in bed and I was trying out one of her favorite games, Genshin Impact, for the first time. I failed to notice that one of the characters, Amber, was a fire type. "It's alarming that you don't see things right in front of you," she said. I explained that it was late, I had a tiring day, and I wasn't focused on the game, I just wanted to relax and enjoy it casually. She said that was no excuse for failing to see what was on the screen, because no matter how relaxed I am, she expects me to be constantly alert.
We argued about this for 24 hours, with her insisting that any reasonably aware person would have noticed Amber's fire attribute, and me insisting that no reasonable person would say such a thing. Since she was ready to break up over it, I eventually had to save our relationship by asking how I could prove that relaxation is a choice, not a disability. She said that if I could play Genshin Impact several nights in a row without making mistakes, her faith in me would be restored. I found this test offensive, but agreed to keep the peace.
Fast forward to today, which began with her telling me she wants to get the creases out of her new shirts, but doesn't know how to use her clothes steamer. I've used a steamer dozens of times throughout my life, so I offered to show her how. Right away, I went to get the steamer, uncoiled the cord, unscrewed the top, and filled the tank with water as I've always done. "Now you just turn it on and wait for the water to boil," I explained. But then, she pointed at it and said, "You went over the maximum fill line." Her tone shift was familiar.
Full disclosure, I didn't know steamers had max lines. I can see why they would, since overfilling one would make the boiling water spit out. To me, that's common sense, which is why I never fill them to the top. I just filled this one more than the line indicated.
I knew where this was going. She wanted an admission of guilt and a promise to do better. But I've used these things so many times without incident. I was 100% sure nothing would go wrong. I begged her, "Please, just trust me, just watch." She stormed out of the room, snapping at me, "I'm not coming anywhere near you while you're misusing that thing."
I switched on the steamer, it functioned exactly as I knew it would, and I ironed her shirt all by myself. I then brought it to her and said, "You see? Nothing bad happened. The line is just for liability purposes." But she replied, "The result doesn't matter. Just because nothing bad happened this time, or the last time you used a steamer, doesn't mean nothing will go wrong next time. By neglecting to study the device and see the max fill line, you took an unnecessary risk. You could have hurt me, you could have hurt yourself. I expect more diligence, and your refusal to own your mistake makes it even worse."
As usual, I can save the relationship if I admit fault. But I feel like I just can't anymore. I truly don't think I made an error here, and even if I had, I'm so tired of apologizing for every misstep, swearing oaths to become better even though I don't think there's anything wrong with me...
My first question to you is, is there something wrong with me? If not, my second question is, what can I do about this other than leaving her? How can I convince her that it's okay for me to be human?
TL;DR - My girlfriend thinks she needs a partner who doesn't make any mistakes. This leads to some pretty severe fights and it's wearing down my resolve, even though we get along great otherwise. What do?


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