How can I run imenu in all project files?

My solution is way too hacky:

A file that you want to have Imenu to access is likely to be tracked by Git.

Use find-file-noselect on all those files (I don't know how to detect binary files with Emacs so limiting on VCS-tracked files is better), and accept the risk of hooks and advices, auto-loading functions, etc.

;;;###autoload
(defun open-project-files-in-background ()
  "Open/find all source files in the background which are tracked by Git."
  (let ((default-directory (vc-root-dir)))
    (save-window-excursion
      (dolist (file (split-string (shell-command-to-string "git ls-files")))
        (unless (find-buffer-visiting file)
          (with-current-buffer (find-file-noselect file)
            (if (equal (get major-mode 'derived-mode-parent) 'prog-mode)
                (bury-buffer)
              (kill-buffer))))))))

;;;###autoload
(defun open-project-files-in-background-maybe (&rest _args)
  "Prepare a project-wide `Imenu'."
  (interactive)
  ;; 'vc-root-dir returns nil when not tracked, so checking if (not
  ;; that it is in a list that contains nil) is enough for both
  ;; (non-nil and in the list of fully opened projects)
  (defvar fully-opened-projects '(nil) "List of project paths, each has all tracked files opened.")
  (let ((git-dir (vc-root-dir)))
    (unless (member git-dir fully-opened-projects)
      (open-project-files-in-background)
      (push git-dir fully-opened-projects))))


(advice-add 'imenu-anywhere :before 'open-project-files-in-background-maybe)

Imenu is for open buffers.

Consider using a command such as find-grep-dired, find-dired, find-name-dired, find-time-dired, or xref-find-definitions.