Doesn't 4G include a time synchronization service for receivers with no GPS; and is the SI second unit (which is currently defined in terms of the cesium decay) const hardcoded in the new system?
Yes, but I believe accuracy is on the order of minutes.
> is the SI second unit (which is currently defined in terms of the cesium decay) const hardcoded in the new system?
Are you saying that a moon second should be defined to be slightly longer/shorter than an earth second to compensate for the relativistic difference? That wouldn't help, since relativity affects all physical processes; if you do that, all your other measures would be off too, including e.g. length (defined as the distance light travels in a given unit of time).
Does the time difference due to time dilation due to relativity change suddenly upon orbiting or landing on another planet spherical reference frame?
The dominating relativistic factor is the gravitational potential (ie general relativity), not the orbital velocity (special relativity), as far as I understand.
GPS compensates for both by offsetting the frequency standard of the satellites’ atomic clocks accordingly.
Now, that's just synchronized with each other, so if the Moon is off by whatever difference in time that's not a problem. It is not like that 4/5G cell is also participating in the same RF environment as cells on Earth.
S-CDMA did have close timing requirements between cells, as far as I know, but the GSM/3GPP family of standards never did.
https://arxiv.org/abs/2402.11150
Cell sites synchronize time with the network, like you phone does but they are talking about Earth time.