It is still sandbox though.There needs to be space for the PCs to make choices with consequences. If events are prescribed to happen when certain milestones are met, and there’s no way of avoiding or changing the substance of those events, I would hesitate to call such an adventure a sandbox. In Kingmaker, that’s basically what happens in adventure book. The PCs have influence over the details, but the broad strokes are fixed. The GM can make it feel like a sandbox, but for it to actually be one, the PCs would need to have actual agency. There’s e.g., no way to avert the war in the fifth book. You get introduced to Irovetti at the start, then Pitax attacks you.
Don’t get me wrong. I don’t think Kingmaker is a bad AP. It was actually my group’s favorite AP of the ones I ran (Council of Thieves, Kingmaker, Rise of the Rune Lords, Shattered Star) and the only one we played to completion. We had a lot of fun building up their kingdom, and some of the events are still memes in my group. However, if I ran it like I’m running my current campaign (an exploration-driven sandbox), it would have broken down. Even that wouldn’t necessarily be a bad thing (since the PCs would presumably then have actual agency), but it’s not what the AP was written to do.
Like... What you are describing is adventure book written with branching paths "oh if in book 1 players do this, book 5 doesn't happen at all or is completely different". If kingmaker wasn't sandbox, then by that definition "Hey party, that GM original country next to you we have never really ever talked about? Well they are attacking you" would instantly prevent homebrew campaign being sandbox.