[Rust] Rust CI no longer works b/c it uses action-rs: Migrate CI away from action-rs/*

[asfimport]

INFRA team deactivated github actions for action-rs, which caused all our CI to stop working.

Since our dependency on it is really small, I propose that we just migrate our builds to not use it.

Reporter: Jorge Leitão / @jorgecarleitao
Assignee: Jorge Leitão / @jorgecarleitao

PRs and other links:

• GitHub Pull Request #9056

_{Note: This issue was originally created as ARROW-11085. Please see the migration documentation for further details.}

[asfimport]

Andrew Lamb / @alamb:
Issue resolved by pull request 9056
#9056