How does this disregard continuity? TNG is, as you discount, over 100 years in the future. This monastery has some weird time crystal thing going on on DSC and may or may not have some time xtal thing going on in TNG in addition to some weird cloning thing that may or may not have been facilitated by the weird time crystal thing. Having seen several minutes of show taking place on this planet & monastery over 2 eras that do not directly contradict what exactly is your problem with the continuity?
Granted I think the time xtals are silly and the whole Pike needs to chose this future or the ability to change it if he wants to take the xtal pretty absurd, I see no reason to assume there is a continuity violation.
To my mind, it just seemed like a clear continuity violation. We've been to Boreth one other time, it was presented as a fundamentally different place then, and the version of Boreth we were shown in this episode had timeless properties that would not have been altered by the intervening time.
Obviously opinions on whether the continuity violation is justified or satisfying will vary (and ultimately I was very satisfied with the story they told, this episode was fantastic). And of course they could subsequently resolve the violation, as they've done with other plot points on this show, and we can already imagine our own fixes if we want (the time-crystals were subsequently shipped off-world after everyone figured out what the monks were up too!).
I just don't understand why Disco keeps setting up such long walks for themselves in this area. Introducing seeming continuity violations that they intend to subsequently resolve with plot gimmicks strikes me as wasted energy. Why change what Boreth is when it's just as easy to go to a Klingon planet other than Boreth? Why shout-out to and disregard continuity at the same time? Who is it for? To the new viewer it's meaningless, and to the established fan it's a distraction. That's the blemish that knocks this down to 2nd best Disco ep -- "If Memory Serves" is on top because it knew how to use it's continuity shout-outs as seamless enhancements of the central story, whereas this episode employed them in ways that took me out of it.
I can get excited about fanboy-continuity-porn, and I can get excited about bold reinventions that cut themselves off from the past and start fresh. Both can be great! What I do want (from any show I watch) is for them to have a clear idea about what they're doing, and Disco's attitude towards continuity has often been very confused.
Though obviously this season has been a thousand times better on this score than season 1, their picture of what they want to do as a prequel has come into much sharper focus (they've truly earned the Michael retcon with how fantastic the story with her and Spock has been). It's hard to know how many of the continuity hiccups have been intentional creative decisions and how many have been behind-the-scenes turmoil. Maybe one day we'll get a full season without a showrunner firing, and get to find out!