AWS Billing alert notification

I have this setup to receive daily budget reports.
https://docs.aws.amazon.com/cost-management/latest/userguide/reporting-cost-budget.html

Otherwise, it is possible to configure repeated notifications of CloudWatch alarms that have gone into alarm as shown in the following document.
https://aws.amazon.com/jp/blogs/mt/how-to-enable-amazon-cloudwatch-alarms-to-send-repeated-notifications/

It sounds like what you need can be done with a budget report https://docs.aws.amazon.com/cost-management/latest/userguide/create-budget-report.html

Set it up to run daily, with an alert threshold of $10k https://docs.aws.amazon.com/cost-management/latest/userguide/budgets-controls.html

I haven't tried it myself, but this guide on a third party site appears to take you through the individual steps https://dev.to/aws-builders/setup-a-everyday-alert-on-your-aws-usage-bill-3c5k

I am not sure you can get daily email fir alert out if the box in the billing budget section.

You may do something custom or instead rely on Budgets Reports, which can be daily: https://docs.aws.amazon.com/cost-management/latest/userguide/create-budget-report.html