They may just be lore at this point, but I've heard stories from friends in the government about older IRS records being kept on punchcards and read into S/360 family machines. The VA is also apparently heavily dependent on a legacy MUMPS[1] codebase, although that could run on more modern machines in principle.
I did contact work with the IRS from '06-'09, on the IMF and BMF (master file system) and I assure you there are no punch cards. Old school main frame assembly yes, but no punch cards.
The last I heard CADE2, the modernized (J2EE) system, had replaced the majority of the IMF functionality (IMF is the core of tax return processing). I'm not completely sure though as I haven't talked to those guys in over 4 years now.
There should be a way to connect a card reader to a newish System Z machine - IBM is famous for its legacy support - likely via some wonky shit over SNA. MUMPS is also fairly portable to new architectures as it was cross platform out of the gate.
S/360 and descendant mainframes have gone through 3 generations of IO technologies: bus & tag channel (parallel copper cabling), ESCON (proprietary 1990s era fibre optic system), FICON (Fibre Channel based). Contemporary System z mainframes only support FICON, whereas card punches/readers were only ever bus & tag. However, I'm aware that some third party vendors offer protocol converters between bus&tag and ESCON, and between ESCON and FICON, (e.g. Optica Prizm) so in theory it is possible you could use a bus&tag-ESCON and ESCON-FICON converter in series to connect your legacy card punch/reader to a new System z mainframe. I don't know if anyone has tried it, so I don't know if it actually works. (I also don't know to what degree the IO code to handle physical card punches/readers still works in contemporary mainframe OSes, although given that virtual card punches/readers are still used under z/VM, it is possible that some of that code might still handle real ones.)
[1]: https://en.wikipedia.org/wiki/MUMPS