How do you install a frost-free garden faucet mid-wall?
...Provide framing/blocking to support it.

Cut a hole stud to stud in the drywall, add blocking between studs (like a one-stud-bay rim joist at a convenient height) and now you have something solid to mount your faucet to.

...And, y'know, repair the wall after - put the insulation back in, repair the vapor barrier if needed, repair the drywall.