Including Short Treks episodes in a chronological rewatch means that the very recently produced Short Treks episode “Q&A”, dealing with Spock’s first day on the Enterprise, comes just before the original pilot for TOS, “The Cage” (and then the first two seasons of DIS before going into TOS proper).
Interestingly, I didn’t find this nearly as jarring as one might think, and while there are absolutely aspects I have problems with (like the external shots of the turbolifts that look like roller coasters surrounded by an absolutely ludicrous amount of open space), I do think it says good things about the care that the modern crew is taking with bringing TOS-era stories into the modern age.
Turbolifts aside, while the DIS version of the Enterprise is absolutely a modern interpretation, it is such a respectful interpretation that it works well for me, even when going from that to the very early ‘60s set from The Cage.
Part of Peck’s DIS interpretation of Spock, of course, was intended to act as a bridge between the more emotional version seen in The Cage and the more reserved version seen in the rest of TOS, and the events of Q&A tie directly into this. Romijn’s Number One is enjoyable, brining a little more warmth to Barret’s, and Mount’s Pike is quite simply an incredible match for Hunter, and it’s even more striking when watching them back-to-back like this.
So yes, as expected, there are differences. How could one expect otherwise, with five decades between the two productions? But even so, it’s quite impressive how well they mesh — at least, in my opinion. I may not agree with every choice the current stewards of Trek are making, but I think it’s clear that they have a lot of love and respect for the universe.