Create test for comp_req__launch_man__multi_start_support

### What

A test for [comp_req__launch_man__multi_start_support](https://github.com/eclipse-score/lifecycle/blob/300173a0e562c9ae75555a83a34dd416416b56a7/score/launch_manager/docs/requirements/requirements.rst?plain=1#L476) is currently missing, but could be easy to add and would lead to a partial verified feature level requirement feat_req__lifecycle__running_processes, too.

Requirement details see link.

### Acceptance Criteria (DoD)

Test in tests/integration/ folder exists and passes which fully verifies this component requirement

### How

_No response_

Start with the linked comp_req__launch_man__multi_start_support requirement in score/launch_manager/docs/requirements/requirements.rst, then inspect nearby tests in tests/integration/. Add an integration test that fully verifies the component requirement and confirm the test passes.

Written by the indexing model from the issue text.