First for an example of what is possible with WASM take a look at Figma, they have a custom vector graphics rendering engine built in C++ compiled to WASM and using WebGL. The performance is incredible for a web app.
WASM is going to take over much of the cloud server market as well. Initially at the “edge” and cloud functions (see CloudFlare workers). But it’s increasingly going to be the standard deployment target. Rust and C++ have first class support for it, over dynamic language such as Python will so be able to run under WASM very soon (Python is just about there).
It’s basically perfect for app plugins as it’s naturally sandboxed. More software will provide a WASM plugin architecture.
Take a look at WASI (https://wasi.dev/), they are working to standardise a system interface for outside the browser.
Finally I also think the embedded market is a possible target for it. Many of the places that currently run an embedded Java VM will potentially use a WASM system in the future.