I tried the following

\setuphead[chapter][align=middle,header=empty,footer=empty]
\setuphead[section][align=middle,number=no]
\setuphead[subsection][align=middle,number=yes,sectionsegments=subsection,conversion=g]
\mainlanguage[spanish]
\definefallbackfamily[mainface][rm][newgardiner][range=egyptianhieroglyphs,
force=yes]
\definefallbackfamily[mainface][rm][quivira][range={ancientgreeknumbers,phoenician},
force=yes]
\definefallbackfamily[mainface][rm][notosanscuneiform][range={cuneiform,cuneiformnumbersandpunctuation},
force=yes]
\definefallbackfamily[mainface][rm][Noto Serif CJK KR][preset=range:korean,
force=yes]
\definefallbackfamily[mainface][rm][quivira][range={greekandcoptic,greekextended},
force=yes]
\definefallbackfamily[mainface][ss][CMU Sans Serif][preset=range:greek,
force=yes]
\definefallbackfamily[mainface][tt][CMU Typewriter
Text][preset=range:greek, force=yes]
\definefontfamily[mainface][rm][Latin Modern
Roman][sc=file:lmromancaps10regular]
\definefontfamily[mainface][ss][Latin Modern Sans]
\definefontfamily[mainface][tt][Latin Modern Typewriter]
\definefontfamily[mainface][mm][Latin Modern Math]
\setupbodyfont[mainface,10pt]
\setuplayout[backspace=2cm,topspace=2cm]
\definepapersize[nice][width=180mm,height=250mm]
\setuppapersize[nice][nice]
\setupinteraction[state=start]
\placebookmarks[chapter,section,subsection][chapter,section,subsection]
\setupinteractionscreen[option=bookmark]
\setupindenting[medium,yes]
\definestructureconversionset [frontpart:pagenumber] [] [romannumerals]
\startsectionblockenvironment [bodypart]
\setcounter [userpage] [1]
\stopsectionblockenvironment
\setuppagenumbering[location=,alternative=doublesided]
\setupheadertexts[\setups{text right}][][][\setups{text left}]
\startsetups[text right]
\rlap{}
\hfill
\sc \getmarking[section]
\hfill
\llap{\userpagenumber}
\stopsetups
\startsetups[text left]
\rlap{\userpagenumber}
\hfill
\sc \getmarking[chapter]
\hfill
\llap{}
\stopsetups
\startfrontmatter
Hello
\completecontent
\stopfrontmatter
\startbodymatter
\startchapter[title=yay]
\startsection[title=wow]
\startsubsection[title=Text]
Bye
\stopsubsection
\stopsection
\stopchapter
\stopbodymatter
\stoptext

What is puzzling to me is the absence of subsection labels. What I expect
is:

1. Yay
   Wow
      α. Text

However, what I've got is:

1. Yay
   Wow
      Text

It's weird that bookmarks and TOC correctly show α before "Text". I don't
know what is wrong. Thank you in advance.