Since the official timeline for the Realms advances with each Season equal to time passing here in the real world
That sounds like an assumption. Princes of the Apocalypse is set in 1491 (as per the hardcover), but the State of Hillsfar document notes that Torin Nomerthal expelled all non-humans from Hillsfar in 1487 DR, while the Harried In Hillsfar adventure begins "two years after the expulsion" (so in 1489 DR). (Not to mention that the event that triggers the Rage of Demons storyline -- Gromph Baenre accidentally summoning the demon lords into the Underdark -- happens in late 1485/early 1486 according to RA Salvatore's book 'Archmage'.)
I suspect the real reason for the Season 4/5 dividing line is that is when AL largely left the Moonsea and turned it over for CCC content.
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Pauper