What to add to paper where another team just beat you to the novelty
It seems you have answered yourself: you found different contributions between your paper and the other one. It's up to you to decide if those differences constitute publishable material and are worth submitting or not really.

The best recipe on how to handle it is, as usual, honesty. You can simply say something like "our findings are in good agreement with recent research...", "recent research came to the same conclusion using a different model...", cite the other paper, compare both and justify why your contributions are important.

This approach is perfectly common in research. Not everything is about novelty.

The reviewers will give you feedback that will provide some clarity and help you how to proceed from there.