for my ps4, I have the forsaken DLC, and I wanted to cross save to my pc (which has Forsaken and Shadowkeep). The question is, will I have access to the Shadowkeep missions and content if my main account is my ps4 account which doesn't have Shadowkeep?
You will not be able to access Shadowkeep-specific content, such as bounties from Eris Morn etc, except on the platform where you purchased the DLC. From the FAQ:
Do my previous game purchases transfer across platforms? Destiny 2 expansions (ex: Forsaken, Shadowkeep) do not transfer between platforms with Cross Save. Destiny 2 Season Passes (ex: Season of the Undying) do move between platforms on the characters they were redeemed on.
I have the same issue, as I own Forsaken and Shadowkeep on Xbox but Beyond Light on PlayStation. I switch back to Xbox sometimes, mainly to pick up missions or purchase certain Exotics.