This is a beautiful question, I appreciate you.
Animittā = Nirodha
The signless state is referring to state of Nirodha, it’s not referring to any state of Jhana. Decent to Nirodha can happen after neither perception nor perception state. Nirodha is a state where all perceptions/feelings/consciousness are ceased. It means there is no being there, only vitality of body functioning. It’s purest state. While one attains Sotapanna/Sakdhagami/Anagami this Nirodha state occurs for short period of time.
After one attains Anagami, a Anagami can enter into this state of Nirodha as many times as he wish. It’s possible only by Anagamis/Arahants. They will do a pre-determination to enter into that state, after that exact duration they will come out. There is a limit on duration one can be in Nirodha, it’s at most 7 days. If it’s more than 7 days the vitality of body disappears.
Suññatā = Nothingness (7th Jhana)
So, Animittā, Suññatā are different states.
There is an excellent discourse of this Sutta by Ven Bhante Vimalaramsi. Highly recommend to go through it, its worth.
MN 43 The Greater Series of Questions and Answers
p.s. Many of his students easily experience different levels of Jhana. And I heard some of his students enter to Nirodha
Finally a quote, the understanding comes only by experience.