Centralized Logging for AWS and Azure

I want to implement centralized logging in AWS for AWS EC2 and Microsoft Azure VM Services.

I want that all logs (both for AWS and. Azure) are stored in AWS.

My Suggestion:
For AWS:

AWS EC2 -> AWS CloudWatch Logs -> AWS Kinesis -> AWS S3 / AWS ElasticSearch.

For Azure:
My Suggestion: Azure VM -> Azure Monitor -> Azure Logs -> Azure Funktion -> AWS API Gateway -> AWS Kinesis -> AWS S3 / AWS ElasticSearch

We have 80% Apps in AWS and 20% in Azure.

Do you have any better idea?

Thanks a lot!