Depends what you mean; but not necessarily.

I am managing an ERP system implemented / went live in 2016. It's working on modern P10 hardware, which was released in 2021. The ERP system is continually updated by the vendor and customized by the client.

Even for COBOL running on an actual mainframe, which I think most HNers would think of 1970s dinosaur, most of the actual machines in production would be pretty new. IBM z16 was launched in 2022.

So they are "legacy systems" in the sense they're not written on a javascript framework which was launched last week, running on lambda instances in AWS :). But they are not "OLD" systems, as such.

Almost certainly yes. The "legacy systems" are likely running on versions of the mainframe with long-term support contracts, whose vendors are committed to providing newer compilers with support for newer versions of the specification as necessary.

When you hear about people being paid $X vs 10x$X to fix some cobol; is there a correlation between the age of the cobol system?