How to build a database that contain only the delta from yesterday
ApexSQL Log can provide the list of transactions made in a specified time period. It has a time range filter where you can specify the last 24 hours, or any other period you want to read. Just make sure you provide enough transaction log backups to cover the specified time range.

ApexSQL Log can also create a redo script for all these transactions, so you can execute it against the new database where delta data will be stored.

What's equally important, if you want this to be a reoccurring job, you can schedule it using ApexSQL Log CLI and SQL Server Jobs.

Here's an example: Automating daily transaction log reading

Disclaimer: I work for ApexSQL as a Support engineer