Orbital data of separated stage becomes corrupted if root part is physicsless.
I'm not sure if I'm running the 32-bit or 64-bit version. It's a 64-bit system (Ubuntu 20, Focal), but it's the version of KSP from Steam: "126.96.36.19945 (LinuxPlayer) en-us".
The attached craft file demonstrates the bug. For clearest demonstration, cheat it into orbit, fire the only stage, and then switch the other craft created by the staging. If you look at the Detailed Orbital Info, it will be switching back and forth quickly to some numbers and 'Nan' values.
A very small amount of experimentation on my part indicates this happens whenever the root part (of the new craft created by staging) is physicsless. I read somewhere (the wiki?) that when physicsless parts become the root part, their physics are turned on. This bug seems to be an instance of that not happening here, or a malfunction of the mechanism that computes the orbital parameters when it does happen.