In both the longest running science fiction shows, Star Trek and Doctor Who, there is an increasing need to just sort of squint and hand wave things away. I'm never going to watch TOS and believe I'm seeing something real, but likewise I don't believe that when watching Strange New Worlds either. At the same time though, I don't treat TOS as a laugh along. It's usually played so straight and so I watch it straight. Same with Strange New Worlds or any Star Trek in-between. But old shows look like old shows. It's not their fault they are old, but they are.
The older a show gets, then the harder it becomes to visually reconcile, either because a lack of time/budget means sets look like, well, sets or a lack of technology in play means special effects can look, well, special. But we wear different hats in a way when we watch different series I think. We have our TOS hats and when we wear them, we enjoy TOS. But we can then put a SNW hat on and enjoy it as being part of the same thing and if the writing and performances are good enough then (for me at least) continuity in aesthetics sort of slides into the background.
I still say that as cool as the episodes in question are, Relics, Trials and Tribulations and the Mirror Universe episodes set up a fan idea that the TOS sets look fine in a modern show. They don't however, IMO. They look good as a bit of kitsch novelty in an episode every now and then, but Trek from TMP onwards has maintained a kind of aesthetic that really doesn't roll with TOS.
But then I just wear the right hat and it's all fine. It's all the same thing in spirit and somehow fans believing it all fits together, despite overwhelming evidence to the contrary, it all kind of does fit together.