Joining new retaining wall to old

Hi everyone,

We are building a concrete sleeper retaining wall across the back of our yard as per the image
At the time of construction the builders ran two wooden sleeper retaining walls either side of the lot.

My question is in building this new wall across the back, should it be free standing on its own or should it connect to these pre-existing two walls either side? I would imagine joined in a giant "C" shape adds structural integrity to the wall but, I am unsure of the method there. Cannot find the information as to how that would be achieved.

Would I dig up the cement and c channel end posts and replace them with corner channels or do you just weld your own c channel to the existing one and take advantage of the post already in use?

Can provide more information if requested

Thanks