So, how does the child process communicate the "property" and the "key" to the calling process?

If that cmd only sets the value in the environment, you will have to call that .cmd in a way very similar (but different to) Get default login environment.

Maybe the following works as another wrapper .cmd file:

@echo off
cd /d %~dp0

call set_prop.cmd db.server.name dbserver

set
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You would then use the output of that intermediate .cmd file as follows from Perl:

my @output= qx(get_property_values.cmd);
chomp @output;

print "Got output [$_]"
    for @output;
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Alternatively, see perlipc.