Can anyone help explain the alliance agreement? I didn't get the point.
This is just my interpretation of the events, maybe the source material explains it better. And I could be 100% Wrong.
From what I gather, the issue is that nations that signed on the "Mankind Declaration" could hypothetically invade non-signatory nations (and also it actually happened with Amidonia) and when those nations retaliate in kind like what Souma is doing right now, they could then invoke the Declaration to hide behind the Empire's superior military might.
Souma is trying to prevent such an event from becoming status quo by making it clear that nations who use the declaration will have to pay compensation to non-signatory nations they invade. In addition to that, the "secret alliance" is to demonstrate to other signatory nations that non-signatory nations can also have close ties with the Empire. Souma sending his country's troops to the neutral (from his perspective) and Mankind declaration signatories, the "Union of Eastern nations" is a signal that the Empire and the Kingdom have developed a close strategic relationship.
This also sets a precedent for other non-signatory nations to do the same should they wish to do so and sends the message to signatory nations that they can no longer hide behind the "Mankind declaration" to initiate hostilities against their non-signatory neighbours, because their neighbours might also be allies with the Empire.