>It’s common knowledge that the military has access to a separate, encrypted, higher-precision GPS signal.

The most militarily-valuable aspect of the military GPS signals is actually the anti-spoofing qualities, rather than the higher precision. Survey-grade GPS gear has been able to achieve centimetre-level precision from the regular civilian signals for several years now, using RF fuckery like tracking the phase angle and other techniques.

To be sure, you want the precision too. NATO countries have M982 Excalibur GPS-guided artillery rounds that are precise enough that you can select not just the building you want to hit but the specific window you want the round to enter.

But the primary benefit of the encrypted signal is that it provides cryptographic assurance that the signal is not spoofed and one can be confident that one's GPS-guided cruise missile or other munition is not being diverted off-course.

Nowadays the military GPS signal has moved from transmitting the legacy "P(Y) code", which is a Cold War-era design, to the "M code" which incorporates several decades' worth of lessons learned in terms of spoofing resistance, cryptographic authentication, etc. It's actually a really neat rabbit hole to climb down.