For each AABB, you take the morton code of the minimum and maximum and store them in the array.
But for sorting and searching, construct a sort key from the pair of morton codes so that the most significant bits are the common prefix of the two morton codes and the least significant bits are the "level" (length of common prefix in bits).
E.g. for a 3d octree with 64 bit keys, you'd have 1 unused bit, 57 = 19 * 3 bits of morton code prefix and 6 bits of level. A 2d quadtree with 32b keys would have 1 unused bit, 26 = 2 * 13 bits of prefix and 5 bits of level.
You could also store just the sort key, but I've stored both AABB morton codes so that I can reconstruct the quantized AABBs for culling.
When you sort by this key, you'll get a linear octree where the beginning of the array is all the AABBs that overlap the subdivision plane, then everything on the left side of the plane and the rest is right side of the plane. When traversing the tree, you need two searches per node to find the entries belonging to this node and to find the split point between the left and the right side.
Having the "level" in the least significant bits works as a tiebreaker in the sorting to ensure that entries closer to the root of the tree are in the beginning of the array.