As far as I know, accessing IndexedDB from WebAssembly only works by passing the data through the JavaScript layer (correct me if I am wrong). So from how I think WebAssembly works, it is likely not any faster then directly doing that in JavaScript. I mean, the storage layer does not have to do any heavy computations, so tunneling the data would be more expensive then what you get from plain js.
When you store the data into an IndexedDB based key-value store, how does the querying work? Do you still use IndexedDBs secondary indexes when a query only matches a range of documents, or does the K-V store has any method to support querying a subset of the data without fetching the whole database state?