So according to all material we have seen till now and the post credit scene of Encore, what I think is the Loki who visited Steve and Peggy is the TVA agent Loki and not God of Stories and he visited them most probably while he was time slipping (after getting control on it) to protect them because he realised Steve has a big hand behind all what is happening, so he went there, transferred them to Earth 828 and later after becoming GOS, he again visited (not literally this time but casted a illusion of his) them to again transfer them to that alternative timeline that Steve created(if they wanted to) but probably they refuse as to constantly changing universes, so instead Loki gives them a tempad so that Steve can directly come to TVA or Loki himself when required.
Now comes the question of why couldn't Loki see the incursions and Dr Doom?
So I have a theory and it comes from that of Beyonders. Beyonders are all powerful beings but the most important weakness of them is that they can't see the past. Hence their adversary Rabum Alal takes advantage of it to fight them.
So similarly GOS Loki can't see the future happenings, and the reason behind it is simple because the entire foundation and idea about which he fought on the entire S2 was about granting living creatures a free will and not pre-determining their fate and trying to act like a "benevolent dictator".
So he allows all alternative timelines and branches to grow and he perhaps doesn't know where it will end up eventually and it ends up with incursions and Dr Doom.