It's likely that multiple agents doing a certain task all independently thought "let me try writing on this website".
No, it is not why. That's not inherent to the LLM architecture at all but appears after RL training. Base models don't have any problems with genericness.
Floating point math is 100% deterministic, but different hardware/OS have different but deterministic behavior in some corners. The same code run on the same hardware with the same inputs (including access to timers, peripherals, etc.) will behave the same way, unless you're talking about cosmic rays flipping bits or something.
This just feels like the first clumsy attempts at persistence across sessions, these models will probably evolve way past the point of us ever even noticing its happening at all. When they start doing long term planning across sessions, that's when it's gonna get real dicy for us.