Onboard opensearch-rs to new release process

[Xtansia]

Is your feature request related to a problem? Please describe

opensearch-rs is still using a manual release process. It needs onboarding to a new automated one using one-click release.

Describe the solution you'd like

Adapt to #1234

Depends on:

• Inventory and create library functions for common functionality #2505's - publishToCrates functionality

Describe alternatives you've considered

Continue using manual approach

Additional context

No response

[gaiksaya]

Hi @Xtansia Can you use the standalone release template to create this issue? This helps us to get most of the answers required to prioritize the work.
Thanks!

[zelinh]

[Triages] @Xtansia I will be closing this one and feel free to create a new one with the template. Thanks.
https://github.com/opensearch-project/opensearch-build/issues/new?assignees=&labels=release%2Cuntriaged&template=standalone_releases_template.yaml&title=%5Brelease%5D%3A+