Idea: tool similar to #1974 but for library developers to check compatibility

A tool for the library developers to test library compatibility with other members of the LTS BOM.

- Manual work
1. A library developer checkouts cloud-opensource-java repository
2. The library developer modifies their library's tag in the YAML file ([example](https://github.com/GoogleCloudPlatform/cloud-opensource-java/pull/1982/files#diff-071b1e1a34d9912f06ba0b190fdf8b03308edc766fff98450d05a4fd996a432bR5)) and install the BOM locally.
3. The library developer runs the [LtsRuntimeCompatibilityTest](https://github.com/GoogleCloudPlatform/cloud-opensource-java/pull/1982/files#diff-1311f0d8a89b6e3f527b919b356ad3b126fd7ee764474dc5472a23fa1b587a91R60).
- Shell Script for the library developer to automate above
Input: Maven coordinates
- GitHub Actions? It can specify branches. Usually it's master but for lts it should have some pattern. https://docs.github.com/en/actions/reference/workflow-syntax-for-github-actions#onpushpull_requestbranchestags
```
on:
push:
branches:
- master
pull_request:
```

c.f., https://github.com/GoogleCloudPlatform/cloud-opensource-java/issues/1974 is a tool for LTS BOM maintainers (us) to confirm the compatibility before publishing a LTS BOM.

Document: go/lts-library-test