Yeah, it couldn't be something simple like a laptop switching to battery mode or anything.
Either way, what your describing sounds like it could be a result of a few things:
0.) Are you using any mods, or have you ever used any in the past?
1.) Turn your power settings, both on the GPU and Windows itself to "Maximum Performance". It could be that you have a power plan on the computer that's just far too conservative for the game. (The new GPU may be the tipping factor.)
2.) When you got the new 16 GB card, did you completely gut the older drivers using DDU and CCleaner? Residual driver files configured for the older GPU may be causing conflicts.
3.) Heat throttling, which should become relatively apparent if you run something like GPU-Z in the background to monitor what the PC is doing in more detail.
- For 2 and 3, these things would likely manifest in other games, though the behavior may not be exactly like it is in CP2077. Do you notice other weirdness in other games, even if it's not as severe?
4.) Background processes taking focus away from the game. Are you using any aggressive anti-virus programs or the like (McAffee, Norton, Comodo, etc.)?