How can I download the whole yaml relationship file from a remotely deployed spicedb instance so that I can visualize the whole relationship and permission in the playground?

Exporting a playground compatible yaml file from a spicedb instance isn't supported. One reason is that the number of relationships in a production or even a fairly used test instance will be significant and beyond the intended scope of the playground's relationship editor. However, you can get the remote schema using

zed schema read

and a subset of relevant relationships with

zed relationship read

and manually write a yaml file representative of the specific state of the spicedb instance you'd like to work on