"The problem I still have with the Perl one-liner is that I don't know how to embed the filename I want to query inside double quotes or how to escape the slash path separators so that it is not interpreted as a regex.
... I wanted a simple "text" or "binary" response ..."

You can just let Perl handle the embedding of filenames/pathnames for you; e.g.

$ pwd
/home/ken/tmp

$ perl -E 'say +(qw{binary text})[-T $ARGV[0]]' /usr/bin/perl
binary

$ perl -E 'say +(qw{binary text})[-T $ARGV[0]]' file_perl
text

$ perl -E 'say +(qw{binary text})[-T $ARGV[0]]' ./file_perl
text

$ perl -E 'say +(qw{binary text})[-T $ARGV[0]]' ~/tmp/file_perl
text

$ perl -E 'say +(qw{binary text})[-T $ARGV[0]]' ~ken/tmp/file_perl
text

$ perl -E 'say +(qw{binary text})[-T $ARGV[0]]' ../tmp/file_perl
text

$ perl -E 'say +(qw{binary text})[-T $ARGV[0]]' ../../../usr/bin/perl
binary
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Note that the commands are identical throughout. You can supply a filename or an absolute/relative pathname in whatever format you want (as an argument to that command).

$ pwd
/home/ken/tmp

$ ls -l file_perl
-rw-r--r-- 1 ken None 105 Aug 13 23:46 file_perl

$ file file_perl
file_perl: ASCII text

$ cat file_perl
/usr/bin/perl: PE32+ executable (console) x86-64 (stripped to external
+ PDB), for MS Windows, 11 sections
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