How to apply the same awk action to different files?

You can apply the files in a for loop:

for file in *.tex;
do
    awk 'ORS=NR%3?" ":"\n"' "$file" > "$(basename "$file")_sorted.tex"
done

Or on one line:

for file in *.tex; do awk 'ORS=NR%3?" ":"\n"' $file > "$(basename "$file" .tex)_sorted.tex"; done

Since you don't specify which shell, go with the more standard basename instead using the shell specific syntax ${file%%.tex}.

If you modify the awk code, can be solved by a single awk process and no shell loop:

awk 'FNR==1{if(o)close(o);o=FILENAME;sub(/\.tex/,"_sorted.tex",o)}{ORS=FNR%3?" ":"\n";print>o}' *.tex

Not a beauty, just insignificantly faster.

Explanations as requested in comment.

FNR (file number or record) is similar to NR (number or record), but while NR is a continuous sequence number of all input records, FNR is reset to 1 when processing of a new input file is started.

A gawk 4.0 only alternative for the FNR==1 is the BEGINFILE special pattern.

awk '
FNR==1{   # first record of an input file?
  if(o)close(o);   # was previous output file? close it
  o=FILENAME;sub(/\.tex/,"_sorted.tex",o)   # new output file name
}
{
  ORS=FNR%3?" ":"\n";   # set ORS based on FNR (not NR as in the original code)
  print>o   # print to the current output file
}
' *.tex