what is built in to perl dist these days that is meant to take the place of CGI.pm?

Short answer: nothing. The philosophy seems to be that since CGI.pm is no longer the de-facto standard for such tasks and has some other drawbacks that it shouldn't be in core rather than there should be something to replace it. A quick search here will show you many discussions about this over the past couple of years so you can look there for the rationale. (Update: Here's one such discussion posted only last month, for example)

My preference these days is for CGI::Lite. It has no non-core dependencies, is lighter (!) and faster than CGI.pm and doesn't require gcc to install because it is pure perl. There are plenty of other CGI implementations out there and there are also a bunch of framework-in-a-box options if you fancy that: Mojolicious, Dancer2, even Catalyst for the brave.

Take some for a spin and see how you get on with them. Folks here will be able to give you ideas but it's a very personal decision which to use depending on whether you prefer speed, resilience, security, flexibility, etc.