No, that's not it at all.
SNW owes almost nothing to the earlier streaming shows with respect to the way they're telling their stories and relating their continuity to TOS. It's pretty much limited to referencing some events in STD.
Which is fine. This is a new, contemporary version of Star Trek. It shouldn't be like the thirty-and-fifty-year old versions.
And it's not errors in canon - it's inconsistencies.
I think it is. Discovery and Strange New Worlds may have a different take on telling stories, but they inhabit the same world. They are linked. Strange New Worlds is a spinnoff of the season 2 characters and Enterprise that appeared in Discovery. Burnham is referenced. How they tell stories has nothing to do with whether or not they are following previous Star Trek canon or not.
The changes forced on the production by Discovery stand.
And as I said before, where TOS had internal inconsistencies (due to the age it was made, and the hectic production schedule, the lack of a standard and the lack of dedicated staff of continuity) and there are the occasional inconsistencies in TNG through Enterprise. But they tried. That is my point. They tried. On occasion a production decision went a different direction (TMP Klingons, TNG Romulans, Ent B, Ent C, Trill) but these were small things. When they wanted to show the 1701, they showed either the original Jefferies design, or the TMP refit. When they made Relics, they quickly and cheaply assembled a set that would fit the look (it was highly inaccurate, though they used some TOS footage to show the original bridge. When the did Trials and Tribbleations, they recreated sets, costumes, and models as close to the originals as they could. For In a Mirror Darkly, they again built sets, costumes, props, and CG models as close to the original as possible. They referenced TOS from time to time. The brought back a number of characters played by the same actors. We had two instances of a connection to the movie era and they put attention into those in terms of sets, costumes, and models. Gary Kerr's work to document the TOS Enterprise in the Smithsonian was directly used for Trials and Tribbleations and In A Mirror Darkly as well as the HD remastered version. They put effort into making it as accurate to the past version of Trek as they could. The Okuda standardized the timeline.
Jump to the Discovery production and it was clear during the first episode that they had not even tried. No attempt was made to link to the established look. Not attempt was made to fit it in the established timeline like the Remastered version did (it used the correct ship version for both pilots and the series). John Eaves put some effort in to create a new Enterprise design that was close to the original, and then the modelers changed it. Change seems to have been the goal of the production. Mudd was a violent criminal instead of a mostly harmless con man. Lorca (him being from a mirror universe can excuse some of this) had things in his office a decade before Kirk was supposedly the first to encounter these things (like the Gorn). They stuck things in as easter eggs just because when they don't fit. The retroed the arrowhead logo where it was not in TOS (it was not the starfleet-wide emblem until TWOK). And the Klingons... yikes. Bad mouth prosthetics, no hair, and this isn't a change from TOS, this is a change from the movies, TNG, DS9, Voyager, and Enterprise. Those series spent a lot of time fleshing out the Klingons into a rich species and Discovery threw it all out the windows (except the language). The elevated every ship to the lofty Starship level and then had a mutiny where the mutineer was convicted. Spock's adopted sister no less, making it a lie when he tells Kirk there has never been a mutiny on a starship. Each one follows the same pattern. A lack of looking up anything (and these days it is so easy online). No research, no attempt at following what came before.
So previous series at least tried (and made mistakes) and Discovery wasn't even trying. Strange New Worlds is trying, but they are guided by what they did in Discovery as much as TOS. So it is better in terms of following the old canon, but in reality the changes are so drastic between the visuals and the story that Discovery and Strange New Worlds are in a reboot world. And I don't know why that word sparks such outrage. When you look up a reboot of any other franchise, the difference in looks and story is exactly what we get with Discovery and Strange New Worlds. BSG comes to mind as does Lost In Space. So why can't it be a reboot? Why doesn't everyone call it a reboot? Well, because CBS says it isn't. Why? Who can say. It is like CBS is scared to admit what they have done when the evidence clearly indicates what they have done.
As a reboot, Strange New Worlds is probably the best Star Trek this generation has ever seen. At its heart, it is the original as Roddenberry envisioned it. That it occasionally strays from TOS canon is irrelevant because it is a reboot of The Cage and a spin-off of Discovery.
And I blame part of it on CBS redoing TOS in broadcast order instead of the production order that Paramount was doing it in. Production order is the only correct way to watch it and not have some of the developmental changes look ridiculous.