Eglot: set imenu-create-index-function without advice

See https://github.com/joaotavora/eglot/issues/1569.

* lisp/progmodes/eglot.el (eglot--managed-mode): Stomp on
imenu-create-index-function conditionally.
(eglot-imenu): Don't check eglot-server-capable here.

* etc/EGLOT-NEWS: Mention change.

etc/EGLOT-NEWS

@@ -45,6 +45,11 @@ thinks responses to inflight requests are no longer useful.  The current
 2026 LSP landscape (especially gopls and ocamllsp) suggests this is
 beneficial and helps servers avoid costly useless work.
 
+** Imenu setup no longer uses advice (github#1569)
+
+Eglot now sets 'imenu-create-index-function' directly without using
+advice, making the integration cleaner and more predictable.
+
 
 * Changes in Eglot 1.21 (11/1/2026)
 

lisp/progmodes/eglot.el

@@ -2364,9 +2364,9 @@ the previous reports for TOKEN.")
     (eglot--setq-saving company-tooltip-align-annotations t)
     (eglot--setq-saving eldoc-documentation-strategy
                         #'eldoc-documentation-compose)
-    (unless (eglot--stay-out-of-p 'imenu)
-      (add-function :before-until (local 'imenu-create-index-function)
-                    #'eglot-imenu))
+    (unless (or (eglot--stay-out-of-p 'imenu)
+                (not (eglot-server-capable :documentSymbolProvider)))
+      (eglot--setq-saving imenu-create-index-function #'eglot-imenu))
     (unless (eglot--stay-out-of-p 'flymake) (flymake-mode 1))
     (unless (eglot--stay-out-of-p 'eldoc)
       (dolist (f (list #'eglot-signature-eldoc-function
@@ -4222,8 +4222,6 @@ for which LSP on-type-formatting should be requested."
 (cl-defun eglot-imenu ()
   "Eglot's `imenu-create-index-function'.
 Returns a list as described in docstring of `imenu--index-alist'."
-  (unless (eglot-server-capable :documentSymbolProvider)
-    (cl-return-from eglot-imenu))
   (let* ((res (eglot--request (eglot--current-server-or-lose)
                               :textDocument/documentSymbol
                               `(:textDocument