You will have to pay extra if you want access to the Dungeons coming during Destiny 2 Year 5. Bungie has provided some additional clarity on what to expect from the post-Witch Queen dungeons, but fans aren't satisfied with the answers, as it all suggests staying up with endgame content is going to be quite a bit more expensive than it's been in the past.
Three dungeons have been advertised for the new year of content. Two will be included with the digital deluxe edition of Witch Queen ($79.99 / £69.99 / €79.99), and one additional dungeon will be included with the 30th anniversary edition ($99.99 / £87.99 / €99.99). As Bungie has made clear today, those dungeons will be offered as separate purchases, too, but will not be included as part of any season pass purchase.
So to have access to all endgame content following The Witch Queen release date, you will need to purchase the expansion itself, the season passes, and either a deluxe upgrade or separate DLC.