To see what has been built in statically, take a look at Config's static_ext setting. This command line'll do that:

perl -MConfig -e 'print $Config{static_ext}'
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It'll be empty, or perhaps have a dl* entry of some sort in it. If there's anything else, well, you have static extensions built in.

You don't compile environment variables into perl, rather you compile in modules that, at initialization time, set keys in %ENV. If you built in Foo, say, the Foo boot code, which is executed when the module is initialized (which for statically built modules is when perl is started), can put things in %ENV.