Found it. Previous WWW::Mechanize solution works OK because forms, there, are encoded wholesale, each and every name and value, regardless. See 455-457.

With new Net::Async::HTTP code, I was trying to be smart, only encoding those text values which obviously require to be encoded. However, another value, a string, simple uid in hexadecimal, sneaked in, which happens to be utf8::upgraded. Then URI module (used by HTTP::Request::Common) produces the whole url-encoded form data in utf-8, as I understand. I don't know if it's expected and documented behaviour, but it's not what server, processing my forms, understands. So solution is to always loop through and encode everything, as in 455-457 lines mentioned.

use strict;
use warnings;
use utf8;
use feature 'say';
use URI;
use Encode 'encode';
use charnames 'cyrillic';

my $uri = URI-> new( 'http:' );

my $ascii_uid_str     = 'abc';      # whatever ascii
my $high_ascii_octets = encode( 'koi8-r', qq(\N{zhe}));
#                     = chr 214;    # (same as above)
                                    # whatever, too, but high-ascii

$uri-> query_form( $ascii_uid_str, $high_ascii_octets );
say $uri-> query;

utf8::upgrade( $ascii_uid_str );    # oops, unexpected

$uri-> query_form( $ascii_uid_str, $high_ascii_octets );
say $uri-> query;


__END__

abc=%D6
abc=%C3%96
[download]