HTML Language Server is provided to Che Theia though the VS Code built-in extension
https://github.com/eclipse/che-theia/blob/727b6c5a1e650a1357652610b48482a9cc5c9bae/generator/src/templates/theiaPlugins.json#L20
When opening any HTML file, Che Theia shows the error notifications, see the attached screenshots.
Open any HTML file in Che Theia.
HTML language features as an autocomplete, hovers, etc. should be provided.

From HTML Language Server output channel:
internal/modules/cjs/loader.js:638
throw err;
^
Error: Cannot find module 'typescript'
at Function.Module._resolveFilename (internal/modules/cjs/loader.js:636:15)
at Function.Module._load (internal/modules/cjs/loader.js:562:25)
at Module.require (internal/modules/cjs/loader.js:692:17)
at require (internal/modules/cjs/helpers.js:25:18)
at Object.<anonymous> (/default-theia-plugins/vscode-builtin-html-language-features/extension/server/dist/htmlServerMain.js:1:473959)
at n (/default-theia-plugins/vscode-builtin-html-language-features/extension/server/dist/htmlServerMain.js:1:158)
at Object.<anonymous> (/default-theia-plugins/vscode-builtin-html-language-features/extension/server/dist/htmlServerMain.js:1:520451)
at n (/default-theia-plugins/vscode-builtin-html-language-features/extension/server/dist/htmlServerMain.js:1:158)
at Object.<anonymous> (/default-theia-plugins/vscode-builtin-html-language-features/extension/server/dist/htmlServerMain.js:1:38535)
at n (/default-theia-plugins/vscode-builtin-html-language-features/extension/server/dist/htmlServerMain.js:1:158)
[Error - 10:08:00 AM] Connection to server got closed. Server will not be restarted.
Note, s.languages.registerOnTypeRenameProvider is not a function is a known upstream issue https://github.com/eclipse-theia/theia/issues/7987. Despite that error, HTML LS starts in upstream Theia.
I've tried with several different versions of html-language-features and the result is the same.
First, need to check this path https://github.com/microsoft/vscode/blob/182db07de2745fe3a6369f4ad80ae930e006a99b/extensions/html-language-features/server/src/modes/javascriptLibs.ts#L12
Most helpful comment
See: https://github.com/eclipse-theia/theia/pull/8224