On Hallowed Ground, a 2e sourcebook, lists the High God as the “over-power” of Krynnspace.¹ Note that On Hallowed Ground is 25 years old, but really every source we might look to is going to be about that old or older. Nothing since has covered crystal spheres, or how separate campaign settings exist in one multiverse, in much detail at all, nor do recent editions (4e or 5e) get into a lot of details about the different levels of divinity and what they mean.
Anyway, overdeities are the ones “over” the other deities² in their particular crystal sphere.³ They set the rules for the sphere, including who gets to be a deity, what that means, what deities have to do, and so on. Ao is an unusually active overdeity, for example, and has changed the rules in Realmspace in response to the gods’ misbehavior on a few occasions. The hypothetical overdeity of Shardspace (Eberron) has an extremely light touch, to the point we can’t be certain they exist, but assuming they do it’s likely that one rule they do have is demanding similar subtlety from the deities that operate there, since we can’t be certain they exist either.
The High God fulfills these roles in Krynn, creating (or, at least, filling out⁴) the basic sphere of Krynnspace, and calling together the gods and telling them what to do. While considerably less active than Ao, the High God is nonetheless relatively active for an overdeity: though they have not interacted with Krynn since its creation except for one solitary time during the All-Saints War, most overdeities don’t have even that one exception.
With the High God as the overdeity of Krynnspace, the various ways in which overdeities differ from other deities answer your questions. Overdeities do not require worship; deities do. Overdeities do not have divine realms in the Outer Planes; (most) deities do.⁵ Overdeities have apparently absolute power over their respective crystal spheres, but are found nowhere else; no deity comes even close to that level of power, but they can operate across many spheres and outside of any.
Applied to the High God, this implies that they can do whatever they wish within Krynn, but have no presence or influence outside of it. Astinous’s history describes only Krynn, not how the wider multiverse developed.
Different books use different terminology: “overdeity,” “overgod,” and “over-power” mean the same thing. I prefer “overdeity” and use it in this answer, but On Hallowed Ground uses “over-power” so I wanted to mention it. Note that I have also argued that what 5e calls “greater deities” are also actually overdeities, and not what were called “greater deities” in previous editions, but this is very much a speculative position at the moment.
Overdeities differ from other deities in so many ways that personally I find it more helpful to think of them as not actually being deities at all, in the D&D sense, but rather being something else entirely above “deity.” (They also likely wouldn’t be considered deities in-setting either, if for no other reason than that almost no one even knows they exist—most overdeities interact solely with the deities under them and no one else.)
A crystal sphere is basically cognate to a campaign setting: each sphere encompasses a solar system more or less. On one of the planets therein, we find a campaign setting we recognize—Realmspace has Abeir–Toril, Greyspace has Oerth, etc. There is probably one overdeity for each sphere, though this is just an assumption we make; plenty of spheres don’t have a known overdeity. It is the differences from one sphere to the next is often seen as evidence for one acting in each.
The actual origins of the spheres and their corresponding overdeities is not known to anyone in the multiverse, most likely, excepting perhaps the overdeities themselves. (You could try asking a leShay but that’s a lot of risk at extremely long odds.) So we don’t know whether the overdeities created the spheres or simply came with them, or how much of the respective sphere was done for them versus what they choose and created.
Some deities have divine realms on non-Outer planes, or simply don’t have realms at all, especially deities of travel or wandering. But they still can be met in person; overdeities cannot.