the case ids are all unique. If you copy cases to new suites then it is a new case with a new, unique test case and independent from each other.
You can reference cases by using the [C123] to reference Test Case 123. This referencing can be done in just about any field in a test case.
If you want to keep the multiple suites then to can make a suite to be the main repository of the test cases. In the new suite, create a case that in each step has a reference to each test case using the [C123] referencing. This would work well as long as the “shared” tests do not change.
Or create only one suite and use test runs and milestones/configurations to cover the tests.
Another possibility - 1 suite to be a repository of shared tests, reference the shared tests as noted already, and any other tests that can’t be shared can get their own suite.