Enforce `open-pull-requests-limit` at core level

### Is there an existing issue for this?

- [x] I have searched the existing issues

### Feature description

Today, the `open-pull-requests-limit` is implemented as a service-level capability rather than within the core logic. This creates unnecessary duplication and complexity for any libraries or tools that rely directly on core functionality, as they must reimplement or work around this constraint independently.

Additionally, this design makes it difficult to test this configuration option in isolation using the CLI, since the enforcement does not exist at the core level where such testing would naturally occur.

Moving this enforcement into the core layer would:

- Ensure consistent behavior across all consumers of core
- Reduce redundant implementations in downstream libraries
- Enable proper testing of pull request limits via the CLI
- Simplify overall architecture and improve maintainability

### Proposed Change:

Introduce enforcement of `open-pull-requests-limit` within the core logic, making it a first-class constraint applied uniformly across all entry points.

Start by tracing the core logic and CLI paths that currently handle open-pull-requests-limit, then compare where service-level enforcement is applied. Done means the limit is enforced consistently through core and can be tested in isolation through the CLI.

Written by the indexing model from the issue text.