Learn German: Was passiert hinsichtlich des Vertrags in einem Schadensfall? - What happens with regard to the contract in a case of damage?

This is because of the preposition hinsichtlich (with regard to). It is a formal preposition of reference that requires the genitive case. Since Vertrag is a masculine noun, the definite article changes to des and the noun takes an -s ending.

Could I also write des Vertrages with an -es at the end?

Yes, absolutely! For many masculine and neuter nouns, you can add either -s or -es in the genitive case. des Vertrags is very common and sounds natural in modern business German, while des Vertrages is equally correct but sounds just a little bit more formal.

Why is there an -s- in the middle of Schadensfall?

That is a linking -s- (often called a Fugen-s). It connects the two distinct words der Schaden (damage) and der Fall (case or event). While the rules for compound nouns can be a bit unpredictable, nouns ending in -en (like Schaden) very frequently use an -s- to connect to the next word.

Why is it in einem Schadensfall (dative) rather than accusative?

in is a two-way preposition. We use the dative case here because the phrase describes a static, abstract situation—the "location" where the rules apply—rather than a physical movement or direction toward a new destination.