[jmillikin]

Application software would still go through the OS native printing APIs. Office or Chrome don't directly interact with the vendor's driver.

As for browser API compatibility, I don't see much point to it since they're mostly designed with the assumption of a JS host. Ideally a WASM driver would export low-level functions to translate from (for example) PostScript to USB packets. Then the underlying native driver (Linux kernel module, Windows dll, etc) runs the WASM and handles all the IO, calling exported WASM functions as needed.