Is it possible to stake Loligo?
Nope. Loligo will be Proof of Work (POW) which means you can't stake it. POS is proof of stake and you can stake those kind of tokens. POW is better though cos it is safer and harder to attack.
How come are many news projects focusing on POS, or plan to switch to that ,while Loligo is going for POW?
Well POS is more eco-friendly to be honest and has some advantages, but also still lacks in some areas.Security wise POW is still safer then POS.
It all depends what type of coin or token you are going to have and the goals project has in mind.
Exactly, since Loligo is going to act like Bitcoin, store of value, Proof of Work makes much more sense then POS.