You wouldn't do
$ pass git init
on the second laptop. Once you have the repo at https://my-private-password-repo.git, you can just do
$ git clone https://my-private-password-repo.git .password-store

in your home directory and will pull automatically create the repo and pull the contents down.

As long as the keys you encrypted the pass repo with on the original laptop is the same as the keys you're using to decrypt with on the other laptop, this should all work.

If you want to use different keys on different laptops, that ... may be possible but I don't know how you would do that.