Earlier quoted context omitted.
"I wonder how this kind of thing is organised, since there's all these jurisdictions." In theory simple. Crowdstrike is doing buisness in state X, so compensation claims will be settled in court in state X. So lots of courts and lawers all around the world, will be quite busy for some time with the case.
It's a B2B tool, which means it's quite likely the contract/license states that all disputes are to be settled in a court appointed by them. This is not valid for consumer disputes, but businesses are free to do what they want. Perhaps this will let them off the hook? OVH is different in that it's actually a French company.
this is not true
just because you write into your contract that something will be settled in a specific jurisdiction doesn't mean it's legally actually the case