I legitimately think a lot of you are too hung up on "Oh my God! Too many TOS characters! It doesn't stand on its own!" I think you (in general not specifically you) all are focusing on the TOS elements disproportionately.
Let me break this down episode-by-episode:
"A Vulcan Hello" --> On the protagonist end: The focus is on Georgiou and Burnham with Saru as a secondary focus. Not TOS characters. On the antagonist end: The focus is on T'Kuvma with Voq trying to get in good with him and L'Rell taking notice. Again, not TOS characters.
"Battle at the Binary Stars" --> Same as "A Vulcan Hello". Burnham has a mental-link with Sarek and we get flashbacks with Sarek and with Burnham first meeting Georgiou on the Shenzou but the focus is clearly on Burnham. The major deaths are Georgiou and T'Kuvma. Sarek is a secondary character through and through. Since he doesn't even show up in person, besides the flashback, I'd even argue he's a tertiary character.
"Context Is for Kings" --> This is very obviously all about the mysterious and unconventional Lorca, with Burnham being instantly accepted by him and with Burnham having to prove herself to everyone else. Also getting us off on the wrong foot with Stamets by showing how much of a prick he is. At least here.
"The Butcher's Knife Cares Not for the Lambs Cry" --> The focus is on Burnham, Lorca, and Stamets. Plus Landry gets killed. And Discovery shows itself off with its nifty Spore Drive by saving those colonists from the Klingons. Big Hero Moment for the Discovery that puts the ship on the map. Meanwhile L'Rell saves Voq from Kol.
Four episodes in and TOS isn't the main focus of anything. Four episodes in and DSC stand on its own just fine. I'm saying this here because the next episode is...
"Choose Your Pain" --> The introduction of Ash Tyler. L'Rell is set up as the main Klingon we'll be dealing with in this series. And the re-introduction of Harry Mudd for the first time (in live-action) in 50 years!!! This is the first time we're seeing Harry Mudd in 50 years, half a century, and he's not even a main character. He's very much a supporting character, who Lorca leaves behind... reinforcing the idea that Lorca is an unconventional asshole. It's less about anything Mudd did and more about what Lorca did. That and L'Rell gets her battle scars, but that must've hurt!
So five episodes in. A TOS character is the tertiary focus in one episode and a TOS character is the secondary focus of another. But it looks like we'll be seeing these two characters on a more regular basis so we have to start thinking of them as DSC characters as well. Luaxana Troi made three appearances on DS9. Gowron actually made more appearances on DS9 than he did on TNG, becoming a recurring character. And Kor, from TOS, appeared three times. That's not even getting into Worf and the O'Briens. So, let me repeat: you have to start thinking of Mudd and Sarek as DSC characters as well. But they're not primary characters. Continuing on.
"Lethe" --> The A-plot is Lorca and Cornwell. The main tension is Cornwell finding out what's wrong with Lorca and him trying to figure out what to do once he knows she knows something is up. Sarek is very much the B-plot and the main source of conflict is on how much his decision effected Michael Burnham. The argument favors Burnham's point of view. We, as the audience, are supposed to side with her, not him.
"Magic to Make the Sanest Man Go Mad" --> Yeah, we've got Harry Mudd, but we've also got Burnham, Tyler, Tilly, high as a kite Stamets... Lorca getting blown up all kinds of crazy ways. Harry Mudd's in it but, let's be honest, who really gives a shit? If this is someone's issue with the episode, all I have to say to them (again, not talking about you) is: lighten up and get over yourself! Also: this is the first time anyone from TOS is a main focus... and he's the antagonist!
"Si Vis Pacem, Para Bellum" --> This is a Saru-focused episode through and through. With a secondary focus on Burnham and Tyler.
"Into the Forest I Go" --> Discovery scores major victories against the Klingons with is 133 Jumps. The focus is on Lorca and Stamets on one end with Burnham fighting Kol and rescuing Cornwell on the other end, while Tyler gets PTSD. How is this focusing on TOS? It isn't. How is this DSC not standing on its own? It is standing on its own.
Then we go into the Mirror Universe. But guess what? So has DS9. So has ENT. And guess what? ENT: the series that so many people on here love to death for reasons I can't figure out why at all, leaned on TOS far more heavily when it went into the Mirror Universe than DSC ever did going into the Mirror Universe. So, if people love "In the Mirror Darkly" but hate the Mirror Universe in DSC because of reasons like "TOS!!!!" then that's some hypocrisy. If you don't happen to like what DSC did, then that's just personal taste. Which happens to not be the same as mine. So, continuing on...
"Despite Yourself" --> Shows the crew of Discovery adapting to the Mirror Universe. Everyone who's focused on: Lorca, Michael, Tyler, and Tilly are all DSC characters. The Mirror Universe itself feels more like the DS9 Mirror Universe than the TOS Mirror Universe. But they do a pretty good job of explaining the Mirror Universe. If you never saw TOS in your life, you'd still be brought up to speed. The audience isn't stupid. "They're in an evil universe!" It's as simple as 2+2. And Culber gets killed by AshVoq. The focus is 100% on Disco. Sure, Lorca claims he wants to go looking for the Defiant but they bring us up-to-speed about that as well. And Lorca doesn't even really give a shit about the Defiant. It's just his excuse to get him and Burnham off Discovery and heading toward the Shenzou.
"The Wolf Inside" --> Burnham et al finally reach the Shenzou, word gets out she's back and that brings us to Georgiou. This is Disco through-and-through. At one point when Burnham has to destroy an enemy outpost, the sole TOS character we see is Sarek -- whose MU counterpart we never even saw in the Mirror Universe! -- and I've already established earlier that I consider him a DSC character as well so we're not going to continue beating this dead horse every time he appears. Sarek is a DSC character now. Get used to it. The main conflict in the scene is between Burnham and Mirror Voq, with AshVoq from the Prime Timeline almost fucking things up.
"Vaulting Ambition" --> All about Burnham, Georgiou, and Lorca. And the Big Reveal that Lorca's from the Mirror Universe. This is 100% Discovery. No TOS, except in one instance when it's outright rejected. Georgiou tells Burnham looking for the Defiant is ridiculous.
"What's Past Is Prologue" --> Lorca's faction vs. Georgiou's faction. Discovery rescues Burnham while she rescues Georgiou in the process.
Back to the Prime Universe...
"The War Without, The War Within" --> Is about cleaning up mess that happened in the aftermath of Discovery's disappearance since it was so strategically important to the Klingon War. The situation is so bad, Cornwell approves of Mirror Georgiou's plans. Nothing TOS-centric in this to speak of.
"Will You Take My Hand?" --> After a detour through the Orion Embassy on Qo'noS, Burnham figures out a way to reach L'Rell thus ending the Klingon War. Everyone's rewarded and this is all DSC-centric until the very end of the episode when Pike's Enterprise shows up... giving Haters to very excuse they crave to sceam "Fanwank!!!" This is Red Meat. The TOS music at the end doesn't help either. I enjoyed the ending but I know this is ammo for the other camp, unfortunately. Then again, the other camp seems pretty joyless when it comes to this series.
And that's it. Dissecting it like that, DSC doesn't lean on TOS anywhere near as much as some people claim. And viewers are brought sufficiently up-to-speed with anything that comes from somewhere else.
The previous shows and movies were in production at the same time. A little bit of moving characters about builds links between them, but none of the older shows were outright dependent on guest characters from other shows for their story. DSC has Burnham rely on Sarek for her backstory. It’s done. Lorca is dependent on the MU for his backstory. Mudd is linked to Lorca. Now it looks like the Disco is gonna borrow the captain of the enterprise. Oh, and section bloody 31 will rock up.
It is impossible to go a single episode of DSC without a link, because the central character is Sareks adopted daughter/ward. This is leaning into it, waaaaay beyond anything ever done in Trek beyond the crossover of Worf and O’Brien to DS9...which was a show set and made at the same time as the shows they crossed over from, and was therefore much more naturalistic. There was writing in show a that intentionally led to events in shows b and c, and threads to be picked up, often with actors and writers crossing over. That’s a tapestry. DSC is a patch. ENT was a bit stitched on the edge and a patch in its later season...but again, at least they matched the material.