I think the point is that you get minimal information for thermal and Active RADAR/LIDAR out to the end of Distant Range (which is stated explicitly in HG2022 as 300,000 km. The rule about Very distant makes any sensor checks formidable. There is nothing in the text that explicitly extends the range of any sensor into the Very Distant or Far bands, it does however create an end to the Distant band at which Thermal and Active RADAR/LIDAR can provide minimal infromation. Other publications might have components or modifications that could extend the range of a sensor and that might mean they can be operated in the Very Distant or Far band.
I'm afraid you are overestimating the omniscience of the Core book.
As far as the Core book is concerned everything over 50 000 km is Distant range, up to infinity.
Core'22, p160:

According to the Core book sensor detail at 100 000 km, 1 000 000 km, and 10 000 000 km is "Minimal" (for Thermal and Active Radar sensors).
Due to historic reasons (2015-16 beta program), Very Distant and Far was later added in HG.
See:
https://forum.mongoosepublishing.com/threads/maximum-range-of-weapons.117984/
The textbox in HG was added in February 2016, when IIRC the Core book was more or less locked.
The Core book does not say anything whatsoever about Very Distant or Far range, because the Core book doesn't know those range bands exist; that is Distant range in the Core book.
Hence the Core book contains no definition of sensor performance at Very Distant range. That absence of evidence should not be seen as evidence of absence of sensor performance at Very Distant range...
HG adds Very Distant range as a subset of Core Distant range and discusses sensor performance at it. The only reasonable conclusion is that sensors actually reach that far.
Ideally that would have been updated in Core'20 or '22, but perfection isn't always attainable.
The only specific example of what can be detected at these new range bands is jump flash. Whilst other books might give a definition of the sensor required for that sort of detection, HG2022 doesn't.
Yes, we can see a Jump flash even at Far range. As that isn't defined anywhere else it was a reasonable place to put it?
This does explicitly not suggest that is the only thing we can see at Far range, as that is one of two cases in the rules text.
My reading of the rules is that None means no information can be determined about the target.
Agreed, but there is no table or text exactly defining sensor information at Very Distant range. There is no rule saying sensor detail is "None" at Very Distant and Far ranges.
That has to be inferred from the text box in HG, saying detection is possible at Very Distant range, hence some information must be available.
HG'22, p26:
Far (over 5,000,000km): At these ranges, sensors can spot the signature of ships making jumps (inbound or out) and can determine only whether a contact is a ship or other similar-sized astronomical body. In either case, sensors are only able to determine the size of the contact to the nearest 10,000 tons.
We are getting information, but restricted to less than normal for "Minimal" (Hot or cold overall + Basic outline) to just a blip and the difference between a ship and a rock (and ±10 000 Dton).
You still need that formidable check to avoid disregarding the blip as a ghost or otherwise irrelevant object and to get a more comprehensive position (and that hint as to its tonnage).
Agreed, and that is a problem for the average Free Trader, but not much of a problem for a decent warship.
If you succeed in the check you can say it is a ship of some type and that it is n*10,000 DTons. It seems odd that you can tell the difference between a 500,000 Dton ship and a 490,000 Dton ship, but not between a 20 Dton launch and a 5,000 Dton cruiser, but that is RAW.
Yes, it's very simplistic, but still quantified so it can actually be used.
The take home is probably that we see no difference between ACSs at Far range.