Only a few citation styles are included in @citation-js/plugin-csl by default. To use the AMA style, you need to download and register it:

let style_ama = Cite.util.fetchFile('https://raw.githubusercontent.com/citation-style-language/styles/master/american-medical-association.csl')
Cite.plugins.config.get('@csl').templates.add('ama', style_ama)

See also a different iteration of this question on GitHub: https://github.com/citation-js/citation-js/issues/231#issuecomment-2282724819.