Discovery’s viewscreen is consistent with the viewscreen of the USS Kelvin. But the bridge is way too big for its time.
The forcefield for the shuttlebay is consistent with the Miranda class and Soyuz class, confirming it was a 23rd century trend.
The lack of food cards for the food processor seen during TOS, and existence of the holocommunicator was advanced for its time. But maybe Starfleet was more technically advance at that time then we were led to believe. Didn’t they have clothing transporters built into sonic showers in TMP that we never saw again, that Ilia used?
As for the interior of the USS Enterprise…maybe Kirk liked the retro style more and saw the update to the bridge unnecessarily dark. While Pike just ripped out the holocommunicator, Kirk ripped out the entire bridge design, and replaced the nacelles.
And as for the timeline being restored, Daniels was a con man, as far as I'm concerned. Otherwise, Archer and his crew would have vanished when the TCW ended and the timeline "reset" itself, since the NX-01 was supposed to be destroyed in its first year.