To be honest, I think the Arika song by Anamanaguchi might be better analyzed in the relative major. bIII is fairly prominent if analyzed in the minor key, especially in the bVI-bVII-bIII (i.e., IV-V-I) moves we find in the pre-chorus. This is basically what’s called a “double tonic complex” (after Robert Bailey’s work), wherein the relative major and minor are somewhat fighting for prominence. In these cases, we typically chart the song in the relative major. The “unintuitive” sequence V/vi to IV can simply be understood as deceptive motion in the relative minor.
The ii chord usually leads to V in common-practice music, but there is an entire school of thought (see the work of Paul Carter, Christoper Doll, and Ken Stephenson) that common-practice music works via “progressions”, whereas rock and pop music employs “retrogressions”. In any event, even the I-V-ii progression could be analyzed by a strict follower of Schenker and classical tonal principles simply as a “back-relating dominant.”
You say you are familiar with harmonic minor, but that of course is a scale not a key. I’ll simply refer you to the Wikipedia article on keys and tonality, which clearly states that, “although many musicians confuse key with scale, a scale is an ordered set of notes typically used in a key, while the key is the center of gravity, established by particular chord progressions.” The first sentence of the Wikipedia article is especially pertinent here: "In music theory, the key of a piece usually refers to the tonic note and chord, which gives a subjective sense of arrival and rest. " For more detail, I refer you to the Cambridge History of Western Music Theory, particularly Brian Hyer’s article on Tonality. The behavior of chords in keys and our perception of keys is indeed a dauntingly elaborate and complex topic.