I am intimately familiar with Star Trek’s canon, including the JJVerse - though I reject the JJVerse in its entirety. So much so that I know that what @starkllr says about Discovery rings true. Discovery is too advanced compared to TOS and the advanced look wreaks havoc with canon, so how do we reconcile the facts on screen so it makes sense to us, with minimal disruption to canon?
Sure, we can fall on the easy explanation: that technology of today is more advanced than it was in the past and the Enterprise has always appeared like it did in Discovery. But that explanation ignores the existing canon. Since canon is whatever appeared on screen, we either need to accept that the Enterprise appeared in its original configuration, was refit to the Discovery version, and refit back to the original configuration, or we need to fill in the blanks here and come up with an explanation to reconcile everything.
Fortunately, I’ve got one. It all starts with Star Trek First Contact.
The Enterprise-E travels back in time to 2063 via the Borg sphere’s temporal wake. Picard and company destroy the sphere, whose remains crash into the arctic. Meanwhile, Picard and crew fix up the Phoenix and its launch center, successfully send Phoenix on its way, and disappear back to the 24th Century.
So while the Enterprise-E crew minimally disrupted the timeline, the remains of the Borg sphere lay in the arctic for nearly a century, until their discovery in 2153. Now, it stands to reason that even though Enterprise NX-01 prevented the Borg from contacting the collective, the wreckage of the Borg sphere remained. There would have to be advanced components remaining undamaged on that ship, components that Earth could study and reverse engineer. The reverse-engineered components, being based off technology some 200 years more advanced, would be fitted into Starfleet vessels. The end result would be what we see on Star Trek Discovery.
So now that we have established how Discovery could appear more advanced than TOS, how do we explain the appearance of TOS and TAS? The answer is that what we see on screen is the state of the galaxy prior to Picard and the Enterprise-E traveling back in time. In fact, every TOS and TAS episode along with all TOS films were affected. However, the law of diminishing returns would also kick in, and the timeline would correct itself by the time the Enterprise-C was launched.
Now, this is all a pretty neat package to explain Discovery’s advanced tech, but there is one fly in the ointment: Trials and Tribble-ations. Fortunately, there is a really easy solution to that one, and that is the Orb of Time. When the Orb of Time sent the Defiant backwards in time it also sent them to the original untouched 23rd Century. The Orb would have also “corrected” their memories of the time period, thus no comments about how the ship and equipment looks different. Upon returning to the 24th Century the Orb would have “restored” the crew’s memories to the new normal, and at the same time bring tribbles back from extinction.
As you can see, I don’t like the easy explanation. It’s more fun to do it this way.