I'm thinking of bypassing my biological dad and communicating with my half-siblings
Why do you want to talk to them?
I feel like my biological family can be closer to each other
It only makes sense that you would want to connect with your extended family now that you know you have them. Even if your parents don't agree with it doesn't mean they can stop you.
My parents should support me and be by my side.
I support your position. I wish you the best of luck