Real world explanation:
The lack of a coherent design language is obviously a misjudgement of the powers that be. Not quite as severe as the complete klingon re-design, but it's obvious they chose the wrong balance between re-design and honouring what came before. Not too surprising with the guy in charge being the same one responsible for the crappy Lost in Space reboot movie. Since everyone already mentioned Axanar (and since both the fan film AND Discovery are so thematically similar, about a pre-Kirk klingon/Federation war), whatever missgivings I have about Axanar, they got the starship design language of the era right. As did the Kelvin movies, which all fit better with TOS than the DIS ships. (Note: This is purely about production design, not the overall quality of those works)
In univers explanation:
The one in-universe explanation I could offer is that the choice of nacelles (round vs. square) has less to do with the actual launching date, and more the tasks of the starships: The Discovery is a mere science vessel, and the Shenzhou was also operating in/near the borders of Federation space. The fleet at the binary stars might be made up of patrol ships. All of them operate near home turf, so they need fast engines, but are in reach for regular maintenance. All of them have square engines. As did for example the USS Grissom. The Enterprise (1701), the Franklin and the Kelvin were all deep exploration vessels. They need longterm reliable, low-maintenance engines. It's more important that they work over years with minimal interruptions, than how fast they are. All of them have round engines.
So far, my personal theory goes:
square engines: Used for travel in Federation borders. Very fast and/or easier to mass produce.
round engines: Longterm durable engines for deep-space exploration
That is, untill the TOS-movies, where old starships get equipped with a new type of engine, that is square, but still usable for long-term service (Enterprise refit, Miranda). Which is then superseeded my a new, transwarp-engine (the Excelsior's nacelles), which is the basis for the "new" warp-speed scale that TNG used, and a predecessor to the mass produced TNG-engines with red bussards/blue glowing lines on the sides.