ci: implement conditional sharding logic in integration tests (googleapis#2692)

## Description

This PR implements test sharding within the integration suite to address
persistent flakiness, resource exhaustion, and long execution times. By
enabling selective test execution based on targeted triggers.

### Implementation

- **Conditional YAML Logic**: Updated .ci/integration.cloudbuild.yaml to
wrap each database-specific step in a conditional block that checks the`
_DB_SHARD` variable.
- **Backward Compatibility**: Maintained support for the original
integration-test-pr trigger by allowing steps to run if `_DB_SHARD` is
unset (empty), ensuring full-suite verification still works.

> Should include a concise description of the changes (bug or feature),
it's
> impact, along with a summary of the solution

## PR Checklist

> Thank you for opening a Pull Request! Before submitting your PR, there
are a
> few things you can do to make sure it goes smoothly:

- [x] Make sure you reviewed

[CONTRIBUTING.md](https://github.com/googleapis/genai-toolbox/blob/main/CONTRIBUTING.md)
- [ ] Make sure to open an issue as a

[bug/issue](https://github.com/googleapis/genai-toolbox/issues/new/choose)
  before writing your code! That way we can discuss the change, evaluate
  designs, and agree on the general idea
- [ ] Ensure the tests and linter pass
- [ ] Code coverage does not decrease (if any source code was changed)
- [ ] Appropriate docs were updated (if necessary)
- [ ] Make sure to add `!` if this involve a breaking change

🛠️ Fixes #<issue_number_goes_here>

Author: NirajNandre