Eve wrote:
"born again" by implication of the words used means born twice, - as Jesus describes in John 3:5. Note that Jesus does not insist that we die first to be regenerated.
In Eve's case she was spiritually alive then by sinning - entered the domain of sin known as "dead in sin" - we are not told whether she is "born again"
The question then is, Did the serpent refer to spiritual death or physical death?
Considering Gen 3.22 I submit that this is directed at Eve, in reference to physical death.
Spiritual death in this context is invalid since even if the body dies the spirit does not.
Thus the serpent refers to physical death in his temptation.
The question is, Did he lie?
Eve went on to live till a ripe old age, therefore it was not a lie at this stage.
As to Eve's spiritual life continuity as "born again" - we don't know. But we do know spiritual life does not end with physical life.
Ergo...."Ye shall surely not die" - was correct.

What is Eve living to a 'ripe old age' as compared with eternal life? It is insignificant. She died spiritually upon the sin, and physically later.