Not quite.
Getting auctex-mode defined modes to become operational feels more
complex than it needs to be -- and I've never understood (30+ years and
counting) as to why Emacs hasn't yet just made Auctex the default Tex
editing package for emacs; I note that we have adopted far newer
packages as the default in more recent times.

Many years ago I made the following my default first line in .tex files:

% foo.tex: -*- mode: LaTeX -*-

and it works as in gets the mode from auctex -- but asking 
describe-function about the mode still shows the one from the emacs
install, not from auctex.




latex-mode is defaliased to 
LaTeX-mode in tex-mode.el
Library is file
/usr/local/share/emacs/29.0.50/lisp/textmodes/tex-mode.elc


latex-mode is an autoloaded interactive compiled Lisp function in
‘tex-mode.el’.

(latex-mode)

Major mode for editing files of input for LaTeX.
Makes $ and } display the characters they match.
Makes " insert `` when it seems to be the beginning of a quotation,
and '' when it appears to be the end; it inserts " only after a \.

Use M-x tex-region to run LaTeX on the current region, plus the preamble
copied from the top of the file (containing \documentstyle, etc.),
running LaTeX under a special subshell.  M-x tex-buffer does the whole buffer.
M-x tex-file saves the buffer and then processes the file.
M-x tex-print prints the .dvi file made by any of these.
M-x tex-view previews the .dvi file made by any of these.
M-x tex-bibtex-file runs bibtex on the file of the current buffer.

Use M-x tex-validate-buffer to check buffer for paragraphs containing
mismatched $’s or braces.

Special commands:

Key             Binding

C-j		tex-handle-newline
"		tex-insert-quote
C-<return>	tex-feed-input

C-c C-s		latex-split-block

M-RET		latex-insert-item

C-c C-b		tex-buffer
C-c C-c		tex-compile
C-c C-e		latex-close-block
C-c C-f		tex-file
C-c TAB		tex-bibtex-file
C-c C-k		tex-kill-job
C-c C-l		tex-recenter-output-buffer
C-c RET		tex-feed-input
C-c C-o		latex-insert-block
C-c C-p		tex-print
C-c C-q		tex-show-print-queue
C-c C-r		tex-region
C-c C-t		latex-insert-block
C-c C-u		tex-goto-last-unclosed-latex-block
C-c C-v		tex-view
C-c /		latex-close-block
C-c ]		latex-close-block
C-c {		tex-insert-braces
C-c }		up-list

C-M-i		ispell-complete-word


Mode variables:
latex-run-command
	Command string used by M-x tex-region or M-x tex-buffer.
tex-directory
	Directory in which to create temporary files for LaTeX jobs
	run by M-x tex-region or M-x tex-buffer.
tex-dvi-print-command
	Command string used by M-x tex-print to print a .dvi file.
tex-alt-dvi-print-command
	Alternative command string used by M-x tex-print (when given a prefix
	argument) to print a .dvi file.
tex-dvi-view-command
	Command string used by M-x tex-view to preview a .dvi file.
tex-show-queue-command
	Command string used by M-x tex-show-print-queue to show the print
	queue that M-x tex-print put your job on.

Entering Latex mode runs the hook ‘text-mode-hook’, then
‘tex-mode-hook’, and finally ‘latex-mode-hook’.  When the special
subshell is initiated, ‘tex-shell-hook’ is run.

This function has :override advice: ‘TeX-latex-mode’.

  Parent mode: ‘tex-mode’.
  Probably introduced at or before Emacs version 18.

[back]

-- 

Thanks,

--Raman(I Search, I Find, I Misplace, I Research)
♈ Id: kg:/m/0285kf1  🦮