Hi Justin
From memory (I don’t have the table in front of me) most of the Azores islands are low density but some places such as S. Miguel I assume will not be.
You can finance properties in Portugal as a foreigner up to 70% LTV but NOT within the Golden Visa level. The Golden Visa requires no recourse to finance within the GV level, anything above the level is fine.
You may accumulate and then apply when you hit the threshold, whatever level it is. Importantly, if you aim for €350K, for example, ALL properties must be qualifying properties for that level, no mixing and matching or the higher level automatically applies.