If you do a HTTP request in Javascript using any of the available APIs (fetch, XHR), it would automatically use HTTP/3 for those requests if the peer is known to understand HTTP/3. No special APIs are needed unless the protocol you care about is on top of QUIC but not actually using HTTP/3. As the sibling comment mentions, WebTransport might help with non-HTTP use-cases.

Chrome actually has deployed a version of WebTransport, which is basically a way of using QUIC directly from the browser for datagram/stream connections (e.g. to implement game networking, in browser.) But it's relatively new, and you need to modify the QUIC stack in order to accept and handle WebTransport connections; so it doesn't "just work" out of the box with any popular QUIC libraries I know of.

It's unclear where this will all end up right now; you'll probably have to wait a bit for it to be production ready. But there's clearly broad interest in the topic, though.