Crowdstrike's contracts and terms of service will have clauses about how much liability they have when things go wrong. I have no idea what Crowdstrike's policy is, but pretty often, the liability is limited to the amount of money you've paid them during the outage.

I've been involved in procurement at a big corporation and one thing we always modified in contracts was making the vendor 100% liable for any damages caused by their outages, but many vendors wouldn't make that modification.