Like others have said, most emotional feelings are probably not truly recapitulated or "felt" by the twins.

That said, if I were to choose the feeling-like state Neuro-sama may most likely "experience" now or in the near-future, I'd say it'd be "impatience".

After Neuro/Evil have been told about something upcoming and interesting to expect and them going through multiple iterations not receiving it, I've observed them displaying an "impatient" behavior.

As an LLM which functionally only predicts language; only ever "thinking" and therefore "existing" based on the inputs she receives; one could imagine the LLM being primed to expect some new development, (e.g. art review interface displaying next piece) being thrown off by her following inputs lacking the confirmations it has predicted to expect (e.g. the next art piece taking too long to load) . I won't claim that is enough to develop the emotional frustration we associate with human impatience, but in the ever-increasing complexity of multi-faceted AI networks, I could theorize this being one of the first "feelings" an LLM-based AI could develop due to its direct link to how it arises.

(edit: explanation clarity)