Apparently, many turtles spend some of their youth in the Sargasso Sea, in the center of the gyre, which has a lot of seaweed shelter and biodiversity, and is warmer. Then they leave when they're stronger.
The center is infertile and can be seeded with fertilizer and algae that can then die off and sink to the bottom of the ocean.
Carbon sequestration is energy negative. The global population of Earth is hurling boulders off a cliff - hoping that a madman Sisyphus decides to lug them back up (to be hurled down again) is not a solution to anything.
Happy to discuss
Another idea is to alter the pH of the ocean.
These topics are not at all simple. They are active areas of research in labs across the world. They have been since the 1980s, and I would not say the solutions are around the corner.
A somewhat new feature in all of this is that venture capitalists are getting into the picture, hoping to make money from developing solutions to the climate-warming problem. Their influence makes it a bit hard to judge what methods might work best. And experts in the field have a right to be ambivalent about receiving research funding from groups that benefit from hiding successful results until patents can be established.