For the current game, the transition is seamless because is free-to-play.
When discussing "cross-buy" for on PlayStation, the situation depends entirely on which game you are playing and which generations you are bridging. While true "cross-buy" (buying once to own on all systems) is rare, Bungie uses Cross-Save and Digital Upgrades to manage your content across PS4 and other platforms. Destiny 2 : PS4 to PS5 (Modern Standard) cross buy ps4 destiny
: If you own a digital version of Destiny 2 on PS4, you automatically have access to the PS5 version. For the current game, the transition is seamless