[Task] Upgrade to latest version of `cargo-release` for publishing to crates.io

## Description
A bunch of stuff changed in their [latest relase](https://github.com/crate-ci/cargo-release/releases/tag/v0.22.0) including how to authenticate. We need to figure out if and how we can use the latest version or replace the tool.

## Change checklist
Add an `x` to the boxes that are relevant to your changes, and delete any items that are not.

- [ ] The feature or fix is implemented in Rust and across all bindings whereas possible.
- [ ] The feature or fix has sufficient testing coverage
- [ ] All tests and examples build and run locally as expected
- [ ] Every piece of code has been document according to the documentation guidelines.
- [ ] If conceptual documentation (mdbook) and examples highlighting the feature exist, they are properly updated.
- [ ] If the feature is not currently documented, a documentation task Issue has been opened to address this.