How does the game compute the nearest unblockaded core province with a port? I am playing as Ming and have cored and colonized Midway islands (picture below). However, the game still says my closest unblockaded core is in Gubbi Gubbi (Australia). How is this computed and why is Midway Islands not my closest port?
You need a) a core and b) a dock (or any better port). Since you cored it, you probably forgot to construct a port in Midway.
The calculation is the same as the distance measurement used for sea attrition. I am not certain if it is affected by trade winds, that could be another reason.
(In older versions you could also rent port access from another country, iirc, but that was removed around 1.5-ish.)