Disco's 23rd century uniforms had shoulder stripes that varied among various ranks, IE everyone below Captain had a certain pattern, Captains had a unique pattern and Admirals had their own. But I'm pretty sure those stripes were strictly decorative and didn't correspond to particular ranks.
To illustrate what @The Wormhole is saying, here are the different Discovery shoulder patterns. Everyone gets the large stripes going around the shoulder seam. As @The Wormhole mentioned, those don't correspond to ranks: men's uniforms always have five, and women's uniforms always have four. For captains, the piping on top of the shoulder between the collar and the sleeve seam becomes gold (or presumably the department colour for non-command division captains?), and then for admirals, the piping at the sleeve head also becomes gold.

but I still find the new versions to be immensely obtuse.
I actually think they're kind acute!

Interesting they have Commodores wearing Flag Officer's uniforms like the Admirals on SNW, as it should be. As opposed to Picard where for some reason Commodores wear standard officer's uniforms.
We've seen that the dress uniforms for flag officers and non-flag officers are identical in design. So I like to think (based on absolutely no evidence whatsoever) that the flag officer's uniform and the standard uniform that we've seen correspond to something like this:


So I'd like to think that if a flag officer had to go out in the field in SNW, that they'd switch to the standard uniform. (And similarly, a non-admiral could wear the style of uniform April wears in certain situations.) We pretty much know from the dress uniforms that the rank insignia on the shoulders correspond exactly to the similar rank insignia on the sleeves. (And yes, now I want to see an episode where April accompanies the crew on a mission, and switches to standard uniform. I wonder if it would retain the navy blue colour, or if it would go to a "standard" division colour? Although knowing television, he'd probably just keep the same uniform we always see him in!

There was a background Tellarite with 3 fingers in the Season 1 finale. But it's a real blink and a miss, so I don't blame you for missing him.
https://twitter.com/gaghyogi49/status/1662519033110073344
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Nice catch!
~~~
So just some random speculation, which I guess I have to spoiler code because it contains information from episode 2 (plus it will help this post to not look so long!

Except for ensign/lieutenant J.G., TMP used the TOS system for non-flag officers. The only flag officer we saw was Rear Admiral Kirk, and he had an extra-wide stripe (in this case, actually three full stripes together as one), with a single full stripe.
So if this also matches TOS, and then if that also matches SNW (I know, big "if"), then potentially the flag ranks could be:
Commodore - 1 extra-wide (season 2 episode 1)
Rear Admiral - 1 extra-wide, 1 wide (speculation based on TMP)
Vice Admiral - 1 narrow, 1 extra-wide, 1 narrow (season 2 episode 2) (although in TOS the narrow stripes are instead broken stripes, and I don't think this one would look that good in that format)
Admiral - 1 wide, 1 extra-wide, 1 wide (all April's episodes)
I believe the Kelvin movies also use the TOS system (with narrow stripes for the TOS broken ones, just like SNW) for the non-flag ranks. I honestly wasn't familiar with the Kelvin flag ranks, but I did some Googling, and this is apparently Marcus's uniform from Into Darkness (it's a photo from an auction site, so forgive the watermark):
There were five pips on the shoulders, so I assume he is a fleet admiral. Now, these stripes don't fit well with the others because it seems it uses only wide and narrow stripes, no extra-wide. But looking at April's insignia, if we map the Kelvin stripes to the next width up, then maybe the last admiral grade could be:
Fleet Admiral - 1 wide, 1 extra wide, 2 wide
But this is very far into speculation, and I don't necessarily expect this is what SNW will use if they ever need to have a fleet admiral. And the other thing is: apparently those stripes that Marcus wore, were also the same stripes that Pike wore in ST2009, and he only had four pips on his shoulders. So it's not even that clear-cut that it's supposed to represent a fleet admiral at all.
I'll stop now. If you're still reading, sorry this was so long, and thank you for your indulgence!

So if this also matches TOS, and then if that also matches SNW (I know, big "if"), then potentially the flag ranks could be:
Commodore - 1 extra-wide (season 2 episode 1)
Rear Admiral - 1 extra-wide, 1 wide (speculation based on TMP)
Vice Admiral - 1 narrow, 1 extra-wide, 1 narrow (season 2 episode 2) (although in TOS the narrow stripes are instead broken stripes, and I don't think this one would look that good in that format)
Admiral - 1 wide, 1 extra-wide, 1 wide (all April's episodes)
I believe the Kelvin movies also use the TOS system (with narrow stripes for the TOS broken ones, just like SNW) for the non-flag ranks. I honestly wasn't familiar with the Kelvin flag ranks, but I did some Googling, and this is apparently Marcus's uniform from Into Darkness (it's a photo from an auction site, so forgive the watermark):

There were five pips on the shoulders, so I assume he is a fleet admiral. Now, these stripes don't fit well with the others because it seems it uses only wide and narrow stripes, no extra-wide. But looking at April's insignia, if we map the Kelvin stripes to the next width up, then maybe the last admiral grade could be:
Fleet Admiral - 1 wide, 1 extra wide, 2 wide
But this is very far into speculation, and I don't necessarily expect this is what SNW will use if they ever need to have a fleet admiral. And the other thing is: apparently those stripes that Marcus wore, were also the same stripes that Pike wore in ST2009, and he only had four pips on his shoulders. So it's not even that clear-cut that it's supposed to represent a fleet admiral at all.
I'll stop now. If you're still reading, sorry this was so long, and thank you for your indulgence!
