To explain what's going on it might be helpful to use underlined bold text to represent strings. So, one can write:

eval 2+2 → 4

and this means if you eval the string 2+2, you'll get the string 4. In perl this is just:

my $x = '2+2';
my $y = eval $x; # $y is the string '4'
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In your original example, what is happening during the substitution s/$match/$replace/e is:

eval $replace → $1 Perl

I.e., the match is replaced with the string $1 Perl, and that is why $text2 contains $1 Perl world.

How about just adding another /e modifier to evaluate the substitution again? Unfortunately this doesn't work because $1 Perl world is not valid perl syntax:

eval eval $replace → eval $1 Perl world → syntax error

When $replace and the substitution is written as:

my $replace = '"$1 Perl"';
$text2 =~ s/$match/$replace/ee;
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the evaluation of the replacement proceeds as follows:

eval eval $replace → eval "$1 Perl"

and because of the double quotes this last eval yields $1 concatenated with a space and the string Perl.