I'd say that some of these criticisms are accurate, specifically the katana one, the somewhat overdone proficiency with swords and guns, and the treecat thing that gets a bit over the top in the later books. (She doesn't actually carry a katana around with her most of the time; she just owns one).
However, some of them don't make sense. For example, looks much younger than she is: Every Manticoran, and quite a few people from the Solarian League and a few other star nations have access to prolong which allows lifespans of several hundred years - so practically
everyone except for those few characters from poor star nations looks younger than they are.
Lots of people have treecat pets. Honor just has the (admittedly poorly-justified) extra special link to Nimitz because she spends so much time around treecats, supposely, although I don't really get how she's spent more time than anyone else.
As you pointed out, the RMN uniforms are all black.
Her name is a play on Horatio Hornblower, which isn't quite the same as normal Mary Sue naming.. usually allusion to a different fictional series altogether is not one of the conventions.
The only authority figure she gets persecuted by for sexual advances is Pavel Young, and he's not really much of an authority figure;
Beating sexism single-handedly on Grayson was a bit much, but on the other hand saving an entire world from nuclear bombardment is likely to make them re-examine notions of your ineptitude, especially when that's going to give them access to your kingdom's technological goodies.
The biggest thing however, is that Honorverse is FULL of Mary Sues. Honor is the main character, and a bit worse, but that's partly just the fact that she's the main character. You don't see the other characters that often, but if you look carefully, except for the occasional person Weber wants to be otherwise, every member of the RMN is a model of professionalism, integrity, and self-sacrifice, not just in willingness to get blown up but in an absurdly good work ethic and generally at least the officers among their enemies are too. The People's Commissioners are, with one exception that strike me off the top of my head, idiots encumbering the Havenite Navy's officers who are generally described as competent.
Unfortunately, Weber waited till a lot later to expose some important things that make Honor less overdone, specifically
Shadow of Saganami and
Storm from the Shadows. In these, Honor is more or less a side character and you get more of a glimpse about how any Manticoran outside of a few villians and the strawman politicals that oppose the Queen and the Centrists, All Manticorans are just a bit overly perfect.
There's also the fact that Honor ususally has a technological advantage by virtue of being Manticoran, and in some cases, she's about to lose when she gets a last-minute rescue.. which is a trait of main characters everywhere, Mary Sue or not.
As to the body counts, they are bad but part of that is that Honor's battles are the ones we see. Since through most of the early-middle books
its safe to assume pretty much any space battle has fairly horrendous casualties. That's just sort of the nature of combat in that universe.
I can understand some of the compaints; Honor is overdone in some ways, but she just doesn't feel Mary Sue-ish to me. Especially the "angsty" things; She mainly just confines them to her romantic life and isn't constantly moaning about them so I don't think they're done in a Sue-ish way even if they might technically fit the trope.