Here's my ultimate unpopular opinion ;-)
I’ve determined the cause behind all of the inconsistency in the various iterations of Star Trek.
We know that Christine Chapel joined Star Fleet in hopes of finding Roger Korby. She found him, but that didn’t pan out like she had hoped. In a weakened mental sate, she transferred her affections to Spock, where they would never be reciprocated. At the end of the 5 year mission, however, it became clear that Spock was leaving her life for good (or at least that was his plan). Her mental health deteriorated rapidly, and she was put in a facility for those with mental illnesses.
From there, everything we see is her fevered dream/nightmare/fantasy. You can’t expect her, a nurse, to have paid a great deal of attention to the shape or even the color of the Enterprise, so when she’s imagines the adventures of Discovery she imagines the Discoprise. For her mind, it’s close enough. Her purpose is to try to find a way to reunite with Spock, even if it’s through imagining a non-existent half sister whom she can pump for information about her half-brother. Details of what the Enterprise really looked like are more or less irrelevant to her.
Other elements are taken from deeper in her subconscious. Her goal with Spock was to start a family, so when she first imagines a future Federation (in which Spock appears, natch) she subconsciously imagines an Enterprise which looks pregnant. Another part of her mind recognizes, however deeply, that she needs mental help, so she imagines a counselor on the ship.
Really, this theory can explain everything. Just like the “It was all a dream” explanation in Dallas when the producers decided to bring back Bobby Ewing, which retconned a season, this can retcon multiple series. The only thing that’s “real” is TOS/TAS.