[LintDiff] simplify CI/CD deployment / change management

Currently, when working with LintDiff, we leverage `rush change` (part of [`rush prep`](https://github.com/Azure/azure-openapi-validator/blob/main/CONTRIBUTING.md#how-to-prepare-for-a-pr-submission-after-you-made-changes-locally)) and `rush version --bump` (part of [deployment to prod](https://github.com/Azure/azure-openapi-validator/blob/main/CONTRIBUTING.md#deploy-to-prod-lintdiff)). This is confusing and hard to get right without good understanding what rush is doing. Recently I had to yet-again clean up the versioning state of the repo in recent PR https://github.com/Azure/azure-openapi-validator/pull/657. For example, one needs to do following set of changes each time deploying to prod:

``` powershell
rush change
#
rush version --bump
#
#
# At this point, this command would fail: rush change --verify
rush change --bump-type none --message "Update changelog via 'rush version --bump" --bulk
git add *
git commit -am "rush change && rush version --bump"
git push
rush change --verify # this should pass
```

The goal of this work item is to stop using these commands: instead of that the documentation will explain how to manually update relevant `changelog.md` and relevant `package.json` files. As part of this work, the call to `rush change --verify` from the LintDiff PR CI needs to be removed.

This work item subsumes large part of the previous work item of:
- https://github.com/Azure/azure-sdk-tools/issues/6141

Related:
- https://github.com/Azure/azure-sdk-tools/issues/7613

@weshaggard @mikeharder @AkhilaIlla @rkmanda @bdefoy FYI