First, it's not being called in list context. That means something else. I call this the multiple argument form.

When you use the single argument form, system expects a shell command and will launch a shell to execute the command*, so

system('echo $PATH');
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is the same as

system('/bin/sh', '-c', 'echo $PATH');
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The shell expands $PATH, and in turn, does

system('echo', '/foo:/bar');
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which is quite different than your

system('echo', '$PATH');
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You must either use the shell

system('echo $PATH');
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system('/bin/sh', '-c', 'echo $PATH');
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or you must do what it would do

system('echo', $ENV{PATH});
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My code is supposed to set $PATH, then run a command on the same line, in the same shell.

You should start by launching a shell, then!

system('PATH=/foo prog arg');
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Or not. This is something you can do yourself quite easily.

local $ENV{PATH} = '/foo';
system('prog', 'arg');
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* — As an optimisation, Perl avoids launching a shell when it's obvious that the shell isn't needed.