Update Rust client quickstart example to match tutorial document

[gefjon]

Description of Changes

Update the Rust client SDK quickstart-chat example to match the code presented in the tutorial, as of clockworklabs/spacetime-docs#162 .

API and ABI breaking changes

If this is an API or ABI breaking change, please apply the
corresponding GitHub label.

Expected complexity level and risk

1

Testing

Describe any testing you've done, and any testing you'd like your reviewers to do,
so that you're confident that all the changes work as expected!

• Ran quickstart-chat locally and:
  • Set my name.
  • Sent a message.
  • Restarted and viewed the message backlog.
  • Sent a few more messages.
  • Exited, deleted my local token, restarted and connected as a new identity.
  • Set my new identity's name.
  • Sent a message as my new identity.

[rekhoff]

Looks clear, well commented, and matches the output from performing instructions in the tutorial clockworklabs/spacetime-docs#162