I've reassigned this to the KDE Store team so they can sort this out for you.
Sysadmin doesn't have the necessary access there to set those up unfortunately!

The server does not recognize the category Cantor (Octave) to which you are trying to upload.

As I see, category for Octave on kde.store.org for this is "Octave Worksheet". Is visible name equals to category name?

Upload from within programs is not possible due to abuse reasons.

As for the visibly naming, I recommend using the category id to display any
content, this should be possible/implemented for some time now (Marco
Martin or Dan Leinir would know for sure).
We can always fill out legacy names though to make it backwards compatible,
but best is to use the ids of the categories.

In T9980#166420, @starbuck wrote:

Upload from within programs is not possible due to abuse reasons.

Could you explain it please? Do you mean, that KNS3::UploadDialog and KNS3::DownloadDialog don't work, because server reject any download/upload requests (except from web interface)?

Exactly that.

I matched all categories to the older naming scheme. Should take a bit
before it becomes visible, though you can see its already used by the
Octave worksheet uploaded.
If anything else needs adjustements, just ping here again.

In T9980#166414, @ronaldv wrote:

We created the missing categories. Please see here: https://store.kde.org/browse/cat/496/

Is everything ok?

When openning the "Get Hot New Stuff" dialog, there are messages in the terminal

org.kde.knewstuff.core: Could not find category "Cantor (Python 2)"
org.kde.knewstuff.core: Could not find category "Cantor (Scilab)"
org.kde.knewstuff.core: Could not find category "Cantor (Octave)"
org.kde.knewstuff.core: Could not find category "Cantor (Qalculate)"
org.kde.knewstuff.core: Could not find category "Cantor (Maxima)"
org.kde.knewstuff.core: Could not find category "Cantor (Sage)"
org.kde.knewstuff.core: Could not find category "Cantor (R)"
org.kde.knewstuff.core: Could not find category "Cantor (Python 3)"
org.kde.knewstuff.core: Could not find category "Cantor (Lua)"
org.kde.knewstuff.core: Could not find category "Cantor (KAlgebra)"

, the list of categories is empty and that one example worksheet that was uploaded is not shown. Do we need to adjust the names/ids of categories in https://cgit.kde.org/cantor.git/tree/src/cantor.knsrc or do we simply need to wait a bit?

In T9980#166420, @starbuck wrote:

Upload from within programs is not possible due to abuse reasons.

If the upload is not possible, should/can the UploadCategories part in https://cgit.kde.org/cantor.git/tree/src/cantor.knsrc be removed?

I think it might be needed to wait 24 hours to replicate on the api-server.
So if by tomorrow there still is nothing, please ping again.