What is the typical pilot to aircraft ratio in military squadrons?
As has been said, there is no one exact rule, but a broad estimate can be easily produced.

There are 12,500 active duty pilots in the USAF, and the service counts just over 5,000 manned aircraft. This will give an overall, rough, ballpark figure of 2.5 pilots per aircraft across the entire force.

Counting aircraft types by pilot seats, one can calculate the total number of pilot seats at around 8,350. About a thousand comes from training aircraft, however.

This gives an overall approximate figure of 1.5 pilots per seat, across the entire USAF.

This is not distributed equally. As mentioned in the comments above, combat units tend to run relatively low ratios. With the recent shortage of pilots, especially ones rated for combat aircraft, it has sometimes fallen below 1:1 in some units. For transport and utility aircraft, there are more crews.