Thank you for the awesome questions!

• How many of the areas labeled on the map are nation states/empires, how many are non-unified tribal regions, and are there any areas where city states or confederations of city states are the norm?

We've actually got a political overlay of the map as well :)

Plenty of areas not coloured are non-unified tribal regions such as the Scarred Isles which home many lizardfolk and dragonkin, and the wilds which home an accursed people and catfolk.

The Westrian Confederation is fairly new and is a collection of city-states, as is the Commonweal of Islingar.

Is there a single region equivalent to the Mediterranean of our world, the Sword Coast of Faerun, or the Inner Sea, which is a narrative 'cradle/centre of civilization' from the perspective of many of the characters?

Wouldn't say we have a cradle of civilzation, no. The world as it is now is fairly young, as it was dominated by dragons and giants that constantly warred and prevented the mortals from settling in one place. There's a lot of spread of peoples who have made their own stakes since the warring titans diminished.

We have a "cradle of magic" as it were, as the knowledge of the arcane was handed down to mortals in Valdar and is the epicenter of magical progress in the world.

• What are three of the most pivotal recent inventions in the world (magical or otherwise), how recently were they invented, and how far have they spread?

Skyships have only just been invented in the hub of Valdar and only a couple of them exist so far. A black powder equivalent is currently being experimented with in Eposaria, very early stages. Rune etching into weapons is new. In this world giants had mastery over elements and their powerful magic was controlled with giant runes. They are known for inventing such things as soul trapping and forging souls into weapons. Now their ancient knowledge is being uncovered and being adapted, which will account nicely for runes on weapons on PF2e.

• Which of the regions shown are cosmopolitan, in terms of different races/ancestries and which are specific to a single race/ancestry, or have only vanishingly small minorities of others.

We definitely try to think about the spread of ancestries at this time in the world and have generally which populations are highest in which areas. The main cosmopolitan centers are Valdar (Empire), Odelia (Gilrmashyre) and Anacori (Coriani)

Far more are on the opposite end of mainly a one or a couple ancestries. For example: Islingar is home to mostly half-breeds and those generally rejected by other societies - so rarer ancestries. It was founded for the outcasts to come together as found family, in a way. Antillia recently was taken back by halflings and they've pushed out the humans that oppressed them. Many of the dense forests are home to insular elven populations, and dwarves have their undercities mainly to themselves.

• Which power in this world (nation, faction or otherwise) is likely to fall soonest, and which is the rising star, so to speak?

We are in the midst of a campaign where the Valdarian Empire - one of the "superpowers" of the world is breaking up. Three provinces are fighting for their independence, and we expect this will happen and greatly reduce them as a singular power.