Are those 1963 comics meant to be the same continuity as the current ones?
Yes, they are. That's the point. DC has rebooted its continuity many times over the decades, but Marvel has always pretended that its universe has been a single continuous whole. Rather than doing discrete reboots to periodically replace or transform the continuity, they just incrementally update the timeframe -- the famous "sliding timescale" -- so that the original stories written in the 1960s are still considered part of the canon even though the period-specific details of them have been replaced and updated. They pretend it's a single continuous whole despite the inconsistencies of detail.
There is no one single way to handle continuity. Different franchises handle it differently. And they rarely treat it as a rigid, all-or-nothing affair. "Reboots" are a fairly modern concept; most long-running franchises have just snuck in continuity changes gradually and expected audiences to either not notice the incremental adjustments or just suspend disbelief about them and play along.
I wonder though, do you ever get to the point that so much has changed that it ceases to be Star Trek. I'm not saying we've reached that point yet. But is there some core to Star Trek that once changed it just becomes another show?
By whose standards? The creators' or a given audience member's? Those are two different conversations. Over the decades, there have always been fans who declared
every new incarnation of Trek to be "not Trek anymore." People said it about the movies. They said it loudly and frequently about TNG for years. And so on. But conversely, there are always going to be new fans who didn't see the earlier versions, people for whom the newer version
is "real Trek" and the older versions are quaint, inaccessible antiques. It's meaningless to even try to ask that question about the audience in general.
The only question that can be asked objectively is, will the
creators of future Trek productions treat a given series as part of the same shared reality as everything else? And to date, the answer has always pretty much been yes. New Trek productions freely draw on elements from every prior Trek production and treat them as sharing a common history, despite their inconsistencies in detail. Kelvin is explicitly an alternate timeline, but one that purports to be branched off of the established Prime continuity and that has drawn on elements from all of it (for instance,
Beyond drew heavily on
Enterprise as part of its backstory). So it stands to reason that future Trek productions will treat
Discovery as part of the same continuity as everything else, no matter what an individual fan may think of it. Spectators don't call the plays.
Does "The Galileo Seven" make sense in a world where Spock was raised with a human sibling?
Does it make sense in a world where he had a human mother, spent at least 4 years at the Academy working alongside humans, and served for over 11 years with other humans on Pike's
Enterprise? Spock's rejection of human perspectives is not a matter of unfamiliarity with humans, but a matter of
choice. He's always been exposed to human points of view but has chosen to reject them as unsuitable for him.
Basically, "Yeah we aged Pike by 17 years so that he can have a hip line about drinking with Georgiou at the Academy, but, uh--Hey look! FASA coordinates!"
