Seems to be a common problem with a variety of causes.
https://www.fiatforum.com/threads/grande-punto-06-not-starting-immobiliser-light-staying-on.303803/
https://www.fiatforum.com/threads/emergency-start-procedure-punto-mk-2.263692/
https://www.fixya.com/support/t2890346-fiat_punto_immobiliser_problem
Hhj, January 2023