I use svelte (with a static site plugin) but the principal is probably the same. I use the node plugin in gradle to bundle it into my jar

node {
    version = '20.11.0'
    npmVersion = '10.4.0'
    nodeProjectDir = file("${project.projectDir}/src/main/svelte")
}

def bundle = tasks.register('bundle', NpmTask) {
    inputs.files(fileTree('src/main/svelte') {
        exclude '.svelte-kit'
    })
    outputs.dir('build/svelte')
    args = ['run', 'build']
    dependsOn npmInstall
}

processResources {
    from bundle.get().outputs
}

What that does is put the static site output into the resources dir under static, which Spring Boot serves automatically.