I think that's pretty reliant on game mechanics, rarities, and release dates.
Objectively, these descriptions aren't directly connected, they're per-unit- so I don't think we can just string them together as if statements in order without further context which confirms that.
Well, I think I'll have to get to lore consistency next on this one (for JP version, sometimes EN version could help with it):
1: The normal Legend Rares and the "other worldly" and "4th-dimensional" meta (lore wise)
- Legend Rares with "a different dimension"/"interdimensional" (consistently using "異次元") meta :
Doktor Heaven (in EN version is "extradimensional"),
Ushiwakamaru,
Miyamoto Musashi,
Legeluga,
Momoco,
Kyosaka Nanaho -> Lore-wise these legend rares belongs to Gacha banners that doesn't have as much creation/destruction/godly type lore as the other.
- The normal Legend Rares with the "4th-dimensional" (consistently using "四次元") meta:
Jeanne (4-dimensional Academy),
Muu (4-dimensional crystal) -> Galaxy Gals are the direct counter units for the High ranking sages (with their Ultra Form coming out at the exact time a new high ranking sage appears just to counter them) so gameplay-wise they holds a special position, while Muu comes from a banner with mass destruction weapons.
2: Special Legend Rares with lore being either "surpassing dimension" (Apotheosis explained), "the origin of everything" or "who have created the world":
Babel,
Lumina,
Gaia -> Lords of destruction/Elemental Pixies who governs the elements of the world (most of them also being galaxy busters)/Literal Gods. Lumina's design also has a symbol that's strikingly similar to Izanagi's crystal.
You can see that the word choice reflects who they are in the most literal way possible. Lower tier legend rares who merely borrows the power of the crystals vs beings that either literally became one with them (Babel), Lumina who born with them or Gaia who is the literal creator God all have power to control the world itself. Well there is an exception being Legeluga (but everything in that banner is kept mysterious lore-wise for they being literal SCPs so we don't talk about them).
Now we have
Izanagi and
Izanami, let's go over them again:
Izanagi: 超次元より舞い降りた始まりの存在 -> "A being of beginning who descended from the superdimension"
Izanami: 超次元より降り立った終わりの存在 -> "A being of finality descends from the superdimension"
"超次元" Apotheosis already translated clearly enough.
Their EN lore is also strikingly similar in weight, being completely different than any other Legend Rares:
"The prelude to all that ever was, descended from a higher plane" and "The coda to all that ever was, descended from a higher plane"
It's all has been about "other world" or "dimension", never "higher plane". They're consistently unique in both Japanese and EN ("superdimension" and "higher plane"), introduced after the Zero World and at the same time as Soractes (Izanagi that is, Izanami is 1 version later) and with all of that their lore is sufficient to say that they're at least above the Zero World (or at least that current layer of the Zero World).
Of course we'll have to go through the Zero World again to reinforce this:
Notice how for Babel they use (超える
Koeru) but for Zero World, even in a Jokingly manner, they still carefully use the word (超越
Chōetsu) instead? If we trust them in their consistency of word choice (which they've been doing a great job at), then Zero World is clearly superior than whatever was there before it or at least Babel and that's all we need (we don't even need any connection here, it's all through word choice alone, actually the lack of connection would place Babel below the Zero World purely because of this), because we're only scaling the Zero World above 5-D spatial dimension after all, that's why it's 7-D spacetime.
Of course we're working under the assumption that the Cats have actually reached the Zero World to begin with (and with how the first subchapter is literally named "Zero Field" and how
the Sage that guided the cats to the current world even said "I want you to find a sage in another world.", it's safe to say that this is indeed the Zero World and not just some random world, for now at least).
"The Edge of Spacetime" directly connects to the Zero World, I think it is just safe to say that it'll upscale whatever-D the baseline is at, to 1-D higher than that
And The high ranking sages being higher than this current layer of the Zero World is still too unclear, so yes this can be set aside for now at least, this would be the most iffy to put in.
So with all of that, it's pretty reasonable to say that battle cats can reach 9-D at the least, and this is not only relying on game mechanics, rarities, and release dates like you said, because this is based on word choice and lore.
Of course, if you still think this is too iffy, then I guess the current meta will be:
Gaia + Babel = 5-D space + 1D time -> 6-D
Zero World is baseline 6-D due to transcends dimensions (placing it at 5-D space and 1-D time) and beyond the edge of spacetime is 7-D.
Izanagi and Izanami is 7-D (should be beyond the Edge of Spacetime, so 2 jumps from 6-D for also being above time), being legend rare so they shared a lore, shouldn't be counted separately from Gaia and Babel, plus "superdimension" indicates their superiority from the normal "dimension". I'd place them at 8-D, above the Zero World if possible.
High ranking sages are at least 7-D due to being on a "far higher dimension", at least on the same level as the Zero World and are also beyond the edge of spacetime.
Or just count "Zero World" and the current "other world" separately, giving Zero World "possibly Low 1-A" and the rest are called "Zero Legend" the above rating.
Whichever you think are the best for now, I'll go with it.
Given the nature of Battle Cats and the way they describe things, it really wouldn't surprise me if it went as high as Low 1-A, but I don't think we have sufficient proof to say for sure. Due to the ambiguity in the Japanese, perhaps we could give Zero World a "Possibly Low 1-A" or something like that.
I'm not sure if it'll be Low 1-A (though it could be), but for now just giving it "possibly Low 1-A" without scaling to any characters at all would be kinda meh, with current information it's already safe to say that it does scale to lots of characters, so Low 1-A or not I think this should be left until it is revealed (and if it is, everything up there will be downscaled quite crazy while the final Sage will be Low 1-A instead... Crazy)
Ah right I forgot, Filibuster's profile will replace an already existing one (that is quite outdated).