Don't know about this series in particular, but the Harrington series
does have a "main thread", and is intentionally written† to not interdepend; the mainline sequence of books by Drake make some references to things happening in the other series, but the books don't expect/require you to have read those series (i.e. the books reintroduce any characters and events that happened in those series that are relevant to the current plot.)
† I find the logic of this series-splitting very interesting; David Drake seems to license out his setting for the creation of, essentially, fanfiction, but fanfiction where he sits in as creative consultant. So other authors create stories in his setting, and he declares them canon.
But, since those stories are not his stories — not created as part of his original series planning — the later novels in the mainline series aren't planned to take these side-sequences into account, but rather just have references to those side-sequences worked in in non-arc-damaging ways as the series allows. Almost like the characters and events from the ascended fanfic are "guest starring" in the main series, as a reward to the audience for reading those side-series and a semi "seal of quality" nod by Drake toward those series.
This isn't a practice I've ever seen anywhere else. The closest might be simultaneously-running TV dramas with different writing teams who lend one-another characters (and their actors) for crossovers, with each writing team acting as the creative consultant for how that character is written by the other team. But even then, there isn't a hierarchical relationship between the two teams, as both teams own their own setting. Also, this setup usually implies that the dramas to be owned by the same production studio.
What Drake does with his settings, is more like when franchise with a valuable IP licenses that IP out for the creation of "licensed" works in adjacent media, on the condition that they sit in as creative consultant for how their IP is being used. E.g. when some random game studio decides to make "a Spiderman game." Except in this case, the IP isn't all that valuable, just an inspiring setting for other authors; and the licensed works aren't in an adjacent medium, but rather also in the original medium, such that they almost "blend in" with the original works.
It's be as if Star Wars were primarily a novel series, but then the various Star Wars Extended Universe licensed novels were still a thing.