So we weren’t 100% sure how it worked, but apparently you can at least take part in the early ranks of the Season even if you don’t own any of the expansions.
I just hit Level 70 on my Necro, just about after finishing Rank 2 of Season 14. 7h in total, everything solo. Was fun enough and the first proper goal was reached.
I had to switch to the Penitent difficulty to progress to Rank 3 and do one Dungeon that was mostly easy with some medium hard parts in between, no deaths, and then continued to just do events for my last 4-5 levels.
And yes, I know full well the real game only starts with the Paragon levels, but for some spontaneous “I am kinda in the mood for Diablo” I’m happy enough I managed to reach this and not lose interest halfway through those 7 hours.