A cloud-native SIEM solution that provides intelligent security analytics and threat detection across systems
Azure Lighthouse is an access delegation service so this can be scoped to only the resource group(s) that you need access to on your customer subscriptions.
You can use RBAC to assign only the level of access required. https://learn.microsoft.com/en-us/azure/lighthouse/how-to/onboard-customer
For Azure Sentinel you may only require access to the resource group where the Log Analytics Workspace is deployed on the customer tenant.
Depending on how you architect your solution will determine the costs, so for example if each customer hosts their own Sentinel service and log analytics workspace then the costs will be on the customer subscription. You can still manage this centrally through your MSSP tenant using Azure Lighthouse.
https://learn.microsoft.com/en-us/azure/sentinel/extend-sentinel-across-workspaces-tenants