While this may not fit each and every one of your examples, I think many of these kinds of spin-offs are often referred to as "revivals".
Unlike spin-offs, in which a television network creates an entirely
new series around an existing character or setting, a revival
reintroduces most or many of the original program's storylines,
characters, and locales, and usually attempts to resolve story arcs
that the original run failed to complete, as opposed to a sequel
that may introduce a new storyline with some of the same characters
after the previous series' story ended. Revivals usually take place at
some point after the original series ends. By contrast, reboots and
remakes may feature many of the original characters differently, but
are usually played by new cast members and without taking into account
events or continuity that occurred during the original series.
Case in point: Star Wars episodes 1-9 is the Skywalker "Saga" (a term coming from Norse Prose), that is an ongoing inter-generational story about the the corruption & absolution of three generations of 'Skywalkers' through the political and metaphysical aspirations of the dark sided Sith Lord, Darth Sidious. In this case you do see the continuation of certain characters and thus previous stories continue to inform and shape the next story, but yet each story also introduces new characters and plots that tend to ring around or "echo" the former story/stories.
And while chronologically speaking of the story itself, you could say that episodes 4-6 & 7-9 are both sequels and revivals, but also episodes 4-6 were actually made first and so technically episodes 1-3 are a prequel story and 7-9 a sequel revival to "the original trilogy"...
Even looking at this Wikipedia paragraph, you can see an attempt to streamline what may be a sequel/spin-off vs the specifically of a revival, which not only seeks to see many previous cast reunite at an older age, but also seeks to address things unanswered from the previous work, as opposed to making a brand new story line that doesn't relate, but doesn't really address if the genre or tone has to be the same.
However it doesn't account for something like Better Call Saul that is mostly a prequel fixating at first on only two characters from Breaking Bad, but slowly,and surely more and more characters, aesthetics, tone, and plot points that relate more directly to Breaking Bad have encroached into it's reality as the final season is walking right up to the line of the Pilot episode of Breaking Bad.
In addition the series also has flash forwards to a time period post Breaking Bad. It remains to be seen how much the future story line plays to Jimmy McGill internally vs how much the last two seasons may reform or reshape any of the narrative of Breaking Bad, but the potential is there. In this case, should it touch more directly on things from Breaking Bad, it would be very hard to technically categorize/define what Better Call Saul actually is, because it's doing a lot of things at the same time and because 'Breaking Bad' is turning into a bigger franchise. Could it be considered a prequel revival in any capacity?
Then we also have something like the upcoming Bosch: Legacy, which is at the very least a direct sequel to Bosch. In this case there is no massive time jump, as the new series was starting to be made immediately after the previous series ended, so the few returning characters are only a little bit older. It will feature at least 3 of the previous' series main/recurring characters, will still take place in many of the same locations/place, but the circumstances of these characters has shifted after the events of Bosch season seven. It also will eventually be incorporating other Michael Connolly works that feature other characters that "cross over" in the author's ongoing crime novel series' universe, such as Renee Ballard.
So again, trying to categorize this might be hard, because clearly the title (ie:"Legacy") is in part referring to a generational passing of the baton, but also potentially what the main older character will leave behind, but it could also be referring to what the main character may still not know about his family history, and thus could still relate to earlier narratives from Bosch. But without a big time jump and no more than three established characters, and considering it takes place in the same location, keeping the same tone/genre, can this be considered a revival too?
Some works may be very complicated to discern because of structure of the story/stories themselves, the order in which an ongoing story/series of related stories are made (because the perspective of "order of ideas" could subjectively change how one looks at it), and/or if genre switching can effect the definition of a revival specifically, despite meeting other criteria.
