But saying the Shenzhou is a "much older ship" when everything about the ship screams more advanced than the Enterprise, is just plain old... wrong.
It's always going to be difficult creating a pre-TOS look with modern production values and a realistic look of what the future will look like to today's audience.  Enterprise walked this line fairly well, the NX-class doesn't look like paper mache sets but still can pass as pre-TOS.  The uniforms look more like modern flight suits that NASA uses, instead of military uniforms.
Discovery (the ship) does a good job at least externally - boxy, ugly, and a Daedalus-like sphere in the middle of the saucer all have a pre-TOS aesthetic.  The interiors don't really jive with me though, but not for continuity reasons.  The interiors of the ships, the uniforms, they all strike me as just generic sci-fi and not really Trek.  It's... boring.  One could argue that the NX interiors were like this as well in the beginning, but by season four they got much more colorful and had some nice TOS homages.
The rest of Discovery's ships definitely look like they fit in with Star Trek Online's era more than anything.  I wouldn't have minded seeing some Kelvin-type ships with some TOS aesthetics (Axanar, despite all their fuckery, did a good job meshing the JJ and TOS universe ships), and maybe even a couple of Enterprise-era ships that Starfleet had to force back into the war - see more of those Intrepid types and maybe even the NX refit due to the desperate situation.
Just so many missed opportunities with this show...