Where are the 1921 census records for Haloch?

Thanks to your extensive research and your GIS and map skills, I may have an answer for you. Disclaimer: I do not read Russian, Ukrainian, Polish, Czech, Slovakian, or Hungarian.

In the historical map at the bottom of your question, I noticed that the green area is labeled with what looks like "Nagy-kaposi járás." In the FamilySearch genealogy site, you can search the catalog for all information about a place (Search > Catalog > Place). When I started to type "Nagyk" in this search, one of the choices was "Hungary, Ung, Nagykapos." And as you say, "Until the Treaty of Trianon, [Haloch] belonged to the Nagykaposi district of Ung county."

The records available for Nagykapos are only church records from the 18th and 19th centuries, but at the top of the page, there is a link that says "Part of Hungary, Ung" and if you click that, it shows the records for Ung, and there are more types of records available. "Census" leads again to a 19th century resource, but under "Public records" there is this:

Общественные документы, 1854-1929
Author: Правление Мукачевской греко-католической епархии. Ужгород

Google/DeepL translation:

Public Papers/Documents, 1854-1929
Author: Board of the Mukachevo Greek Catholic Diocese. Uzhgorod

Clicking on this link gives a page with the following description:

Микрофильмированное издание рукописей в Государственном архиве Закарпатской области в г. Ужгороде, Украина.

Public records (lists of citizens and homeowners, lists of students, census tables, miscellaneous documents) for multiple locations in Ungvár, Ung, Hungary and Ung district; later Užhorod, Podkarpatská Rus, Czechoslovakia; now Uz︠h︡horod, Zakarpatti︠a︡, Ukraine and for Munkács, Bereg, Hungary; later Mukačevo, Podkarpatská Rus, Czechoslovakia; now Mukacheve, Zakarpatti︠a︡, Ukraine. Text in Russian and Ukrainian.

Фонд 43, опись 1, дела 15, 182, 1471 -- Фонд 43, опись 7, дело 408 -- Фонд 43, опись 10, дело 52 -- Фонд 151, опись 17, дела 1363-1372 -- Фонд 1026, опись 1, дела 314, 321, 406, 587-591.

Google translation:

Microfilmed edition of manuscripts in the State Archive of the Transcarpathian region in Uzhgorod, Ukraine.

Public records (lists of citizens and homeowners, lists of students, census tables, miscellaneous documents) for multiple locations in Ungvár, Ung, Hungary and Ung district; later Užhorod, Podkarpatská Rus, Czechoslovakia; now Uz︠h︡horod, Zakarpatti︠a︡, Ukraine and for Munkács, Bereg, Hungary; later Mukačevo, Podkarpatská Rus, Czechoslovakia; now Mukacheve, Zakarpatti︠a︡, Ukraine. Text in Russian and Ukrainian.

Fund 43, inventory 1, files 15, 182, 1471 - Fund 43, inventory 7, file 408 - Fund 43, inventory 10, file 52 - Fund 151, inventory 17, files 1363-1372 - Fund 1026, inventory 1, cases 314, 321, 406, 587-591.

DeepL says "State documents," "Subcarpathian Rus," and "Transcarpathian district" instead of "Public records," "Podkarpatská Rus," and "Zakarpatti︠a︡" but otherwise its translation is similar.

This title looks promising. Inside it are the following entries among others:

Ф. 43, о. 1, д. 15 Список жителей 1920
Ф. 43, о. 1, д. 182 Список польских подданых 1920

Translation:

F. 43, o. 1, d. 15 List of residents 1920
F. 43, o. 1, d. 182 List of Polish citizens 1920

The first of these looks like a sort of a census. It's written on what looks to be repurposed agricultural census forms with column headers for rye, millet, oats, etc. that have been overwritten with what looks like and what machine translation tells me could be "15 and up" and "15 and below." The name column seems to have mostly male names such as Ferencz and Janos, so this could be a 1920 census of heads of households with tallies of adults and children.

There are other filmed rolls that are "Списки домовладельцев" or "lists of homeowners" but no date is given in the metadata; you'd have to click through to see whether the dates apply.

Note that while all of these documents have been digitized, none of them have been indexed, so you will have to (a) be willing to examine every page, (b) be able to read the handwriting, and (c) be able to translate or use machine translation or find a translator. Even then, you may still not find your town and/or family.