The core SQLite project releases only "vanilla JS" distributions which are independent of any given developer-side toolchain. However, a community-maintained npm-based distribution of the SQLite3 WASM components can be found at @sqlite.org/sqlite-wasm.
It can be installed from a command-line shell using:
$ npm install @sqlite.org/sqlite-wasm
An introduction for using it, including instructions for use with Vite, can be found here.
Feedback on the package, as well as suggestions (or patches) for improvement, are welcome via GitHub Issues.
Note that the npm module sub-project covers only the npm-specific components, so tickets about other components should not be posted there. To request support for, or report problems with, the non-npm-specific pieces, please use the SQLite forum.
Sidebar: despite being "community-maintained," it is an official sub-project of the SQLite project. It is maintained by third-party volunteers for the simple reason that none of the SQLite maintainers use npm-based tools, so cannot directly offer support for them.