The 1PPS output may have that much jitter (due to it being clocked synchronously with the module's system clock) but I believe there is usually a way to query the device for the error between the 1PPS signal and the actual idealised pulse time.
Sylvain Munaut made a project using a high resolution TDC/time of flight converter to discipline another clock against the GPS idealised pusle time. I can't find a link right now unfortunately.
Yes, this feature exists, but it's usually only present on GPS modules that are sold specifically for time keeping instead of location tracking, such as the uBlox LEA-M8T.
They are much more expensive, think $100 instead of $10.
The 1PPS output may have that much jitter (due to it being clocked synchronously with the module's system clock) but I believe there is usually a way to query the device for the error between the 1PPS signal and the actual idealised pulse time.
Sylvain Munaut made a project using a high resolution TDC/time of flight converter to discipline another clock against the GPS idealised pusle time. I can't find a link right now unfortunately.