Enhancement: Add `reproducibility-failed` status to `test_model()`

[nilsmechtel]

It would be beneficial to introduce a new statuslike reproducibility-failed to ?bioimageio.core.test_model(). Currently, models that pass the initial metadata check but fail later tests are categorized under the same broad status valid-format`.

Adding this intermediate status would allow us to differentiate between two distinct failure cases:

• valid-format: The model passes metadata checks but fails core execution (e.g., environment setup or Python code errors).

• reproducibility-failed (New): The model has a working environment and executes successfully, but the output does not meet the required reproducibility threshold.

• passed: The model passes all checks, including reproducibility.

This change would help identify models that are "functional" even if they aren't perfectly reproducible.

For BioImage.IO: The inference test CI is currently used as a temporary workaround to identify models work in the test run functionality.

[FynnBe]

I am reluctant to add this additional status for these reasons:

• if it runs, but we have no idea if the output is correct, we should not advertise to use the model anyway. I know we care about this distinction in terms of trying to fix the model, but the reason a model is only 'valid-format' is clear when looking at the test summary.
• failed, valid-format, passed reflects the test stages of testing with spec ('validate-format' and with core 'passed'), it is not supported to test inference independent of reproducibility.
• another status adds complexity, the 'order' of the different statuses is not clear (is 'reproducibility-failed' worse or better than 'valid-format'?

I can add the bioengine to the compatibility overview at https://bioimage-io.github.io/collection/latest/compatibility/#compatibility-by-resource if you want. Maybe that can help assessing models from a non-model-specific maintainer point of view.