I think several of your arguments are really strong. But I think that there's a flaw baked into the term 'Mary Sue' that makes it difficult for me to justify its continued use: it's built on a limited understanding of how varied the goals of fiction can be, and that the speaker will always be able to recognize those goals.
My husband almost exclusively reads power fantasies that allow the hero to solve every problem easily through cleverness and kindness. Every hero is overpowered. There's almost no tension. There being no tension despite the ridiculous stakes is the POINT, because he wants to dream that fixing the world without destroying himself is possible.
I just finished reading Anne McCaffrey's Dragonsinger and Dragonsong to my teen. The heroine is universally beloved, except when being bullied or abused, and 1/3 of the second book is scene after scene of people telling her the abusers were wrong, and she is good, and talented, and gets to skip all the work other characters have to do because she's so special, etc. (She is SUCH a Mary Sue! Fails half the arguments you gave!) My teen would get so excited that we'd have to pause so they could rock and squeal, because their self-confidence is through the floor and they DESPERATELY need to watch someone learn to believe in herself again.
20 years ago I used to read whump fic (what's now called hurt/comfort) where the main character's 'personality' was 'is a victim'. (My standards have risen since them, but only slightly ;) There was no tension, no drama, just noble suffering and then someone comforting them. Those guys were definitely Mary Sues, but they were also perfect vessels for me to project my pain and angst onto, so I could get some distance and process it.
'Mary Sue' started as a way of mocking mostly young, mostly female, authours for writing stories that were 'bad'. But usually they were mocking stories where the arc was 'character triumphs over her insecurity and is taught she is lovable and valuable with the series events as a backdrop' by saying 'this story is so bad because the main character acts like a stupid 13 year old and the battles are afterthoughts that are solved too easily'!
Someone has to understand the goals of a story before they can judge whether the main character works.
I can't judge romance novels because I'm a romance-repulsed aroace, and I do NOT understand why they're doing ANY of what they're doing. I can't judge my husband's isekai protagonists, because solving all the world's problems on my own is a nightmare, not a fantasy, for me.
I CAN judge Menolly, from Dragonsong, and she's PERFECTLY designed to find believing she has value a struggle, despite being a once in a generation musical talent. Which is the exact arc that so many 'Mary Sue's get derided for. (She's also written by a talented authour, and those books are great. They're just written for young teens.)
I can also judge Ender. Ender's Game is about how dehumanizing the enemy breaks something inside those who do it, about whether war crimes can be defendable, about how gifted tracks can isolate and warp kids, and a dozen other really thorny ethical problems. It's a tragedy, and ends pretty much identically to The Lord of The Rings - with Ender too broken to return to society and needing to travel across the waters/space. Ender is perfectly designed to headline that tragedy. He's a gifted kid who cares greatly about other people, but with that slight distance that neurodivergent people often have. Which is taken advantage of to twist him into a mass murderer, while also leaving him able to mourn what he's done. Every victory is HORROR, not a sign of how great Ender is!
I agree that "this character is so perfect it becomes a major flaw in the story" can be a meaningful criticism. I've dropped a lot of books because I found them boring for that very reason.
But I don't think "Mary Sue" is the correct term for that concept. Because it has, right from the beginning, been about judging characters by the wrong standard. It's about assuming that 13 years have the same level of self-knowledge as adults, and aren't writing 'perfect' characters that people hate 'for no reason' because they don't understand why people hate THEM. It's about assuming that since I read superhero fanfic, I must care about the fighting and powers. It's about assuming that if a character has no challenges in the areas that the speaker cares about, then they have no meaningful challenges at all.
Which is something you also recognize, obviously - I saw the point about Project Hail Mary! But I don't think it is something that can be worked around - it's foundationally baked into "Mary Sue."