No matter how much the weather makes you feel like gardening (or perhaps not…), there is nothing tracing back to seeds, roots, or things buried far within the dirt with this idiom.
If you have a belief that is held deep in your core, it is “deep-seated”—as in seated deeply within your heart. (Note, there’s a hyphen present since these two words are combining to become an adjective.)
You don’t want to bury your seeds too deeply or they won’t grow. The same goes for this idiom. No more deep seeding, everyone. “Deep-seated” is the way to go.