Hongyi Zhao <hongyi.zhao@gmail.com> writes:

> Then I open the following tex document in Emacs
>
> ```
> \documentclass{paper}
> \usepackage{braket}
> \begin{document}
>    Some testing comes here.
> \end{document}
> ```
>
> and enable Eglot (M-x eglot), but I find that Eglot Failed to do the
> completion for commands defined in specified loaded packages for
> auctex. But TeXstudio doesn't have this problem.

Do you know what Eglot is?  It's an LSP (Language Server Protocol)
client which requests completions, documentation, etc. from an LSP
server.  I doubt there is a LaTeX LSP server.

You can use company-mode with capf (and dabbrev) backend with auctex to
get completion popups, see this screenshot: