Call browser functions via `browse-url'

This is in order to apply `browse-url-transform-alist'.

* lisp/net/browse-url.el (browse-url-with-browser-kind)
(browse-url-button-open, browse-url-button-open-url):
* lisp/net/shr.el (shr-browse-url):
* lisp/net/eww.el (eww-browse-with-external-browser):
* lisp/gnus/gnus-sum.el (gnus-summary-browse-url):
* lisp/emacs-lisp/package.el (package-browse-url): Let-bind
`browse-url-browser-function' and call `browse-url'.

lisp/emacs-lisp/package.el

@@ -4694,8 +4694,10 @@ DESC must be a `package-desc' object."
   (let ((url (cdr (assoc :url (package-desc-extras desc)))))
     (unless url
       (user-error "No website for %s" (package-desc-name desc)))
-    (if secondary
-        (funcall browse-url-secondary-browser-function url)
+    (let ((browse-url-browser-function
+           (if secondary
+               browse-url-secondary-browser-function
+             browse-url-browser-function)))
       (browse-url url))))
 
 (declare-function ietf-drums-parse-address "ietf-drums"

lisp/gnus/gnus-sum.el

@@ -9410,7 +9410,7 @@ See `gnus-collect-urls'."
                            (concat "#" target)))))
       (concat host (string-truncate-left rest (- max (length host)))))))
 
-(defun gnus-summary-browse-url (&optional external)
+(defun gnus-summary-browse-url (&optional secondary)
   "Scan the current article body for links, and offer to browse them.
 
 Links are opened using `browse-url' unless a prefix argument is
@@ -9431,9 +9431,11 @@ default."
 				 (gnus-shorten-url (car urls) 40))
 		  urls nil t nil nil (car urls))))))
     (if target
-	(if external
-	    (funcall browse-url-secondary-browser-function target)
-	  (browse-url target))
+        (let ((browse-url-browser-function
+               (if secondary
+                   browse-url-secondary-browser-function
+                 browse-url-browser-function)))
+          (browse-url target))
       (message "No URLs found."))))
 
 (defun gnus-summary-isearch-article (&optional regexp-p)

lisp/net/browse-url.el

@@ -1000,7 +1000,10 @@ opposite of the browser kind of `browse-url-browser-function'."
                    browse-url-secondary-browser-function
                    #'browse-url-default-browser
                    #'eww))))
-    (funcall function url arg)))
+    (let ((browse-url-browser-function function)
+          (browse-url-handlers nil)
+          (browse-url-default-handlers nil))
+      (browse-url url))))
 
 ;;;###autoload
 (defun browse-url-at-mouse (event)
@@ -1788,17 +1791,19 @@ clickable and will use `browse-url' to open the URLs in question."
                                          browse-url-data ,(match-string 0)))))))
 
 ;;;###autoload
-(defun browse-url-button-open (&optional external mouse-event)
+(defun browse-url-button-open (&optional secondary mouse-event)
   "Follow the link under point using `browse-url'.
-If EXTERNAL (the prefix if used interactively), open with the
-external browser instead of the default one."
+If SECONDARY (the prefix if used interactively), open with the
+secondary browser instead of the default one."
   (interactive (list current-prefix-arg last-nonmenu-event))
   (mouse-set-point mouse-event)
   (let ((url (get-text-property (point) 'browse-url-data)))
     (unless url
       (error "No URL under point"))
-    (if external
-        (funcall browse-url-secondary-browser-function url)
+    (let ((browse-url-browser-function
+           (if secondary
+               browse-url-secondary-browser-function
+             browse-url-browser-function)))
       (browse-url url))))
 
 ;;;###autoload
@@ -1806,8 +1811,10 @@ external browser instead of the default one."
   "Open URL using `browse-url'.
 If `current-prefix-arg' is non-nil, use
 `browse-url-secondary-browser-function' instead."
-  (if current-prefix-arg
-      (funcall browse-url-secondary-browser-function url)
+  (let ((browse-url-browser-function
+         (if current-prefix-arg
+             browse-url-secondary-browser-function
+           browse-url-browser-function)))
     (browse-url url)))
 
 (defun browse-url-button-copy ()

lisp/net/eww.el

@@ -2257,7 +2257,8 @@ external browser."
   (setq url (or url (plist-get eww-data :url)))
   (if (eq 'external (browse-url--browser-kind
                      browse-url-secondary-browser-function url))
-      (funcall browse-url-secondary-browser-function url)
+      (let ((browse-url-browser-function browse-url-secondary-browser-function))
+        (browse-url url))
     (browse-url-with-browser-kind 'external url)))
 
 (defun eww-remove-tracking (url)

lisp/net/shr.el

@@ -1097,9 +1097,9 @@ When `shr-fill-text' is nil, only indent."
   (mouse-set-point ev)
   (shr-browse-url nil nil t))
 
-(defun shr-browse-url (&optional external mouse-event new-window)
+(defun shr-browse-url (&optional secondary mouse-event new-window)
   "Browse the URL at point using `browse-url'.
-If EXTERNAL is non-nil (interactively, the prefix argument), browse
+If SECONDARY is non-nil (interactively, the prefix argument), browse
 the URL using `browse-url-secondary-browser-function'.
 If this function is invoked by a mouse click, it will browse the URL
 at the position of the click.  Optional argument MOUSE-EVENT describes
@@ -1110,8 +1110,9 @@ the mouse click event."
     (cond
      ((not url)
       (message "No link under point"))
-     (external
-      (funcall browse-url-secondary-browser-function url)
+     (secondary
+      (let ((browse-url-browser-function browse-url-secondary-browser-function))
+        (browse-url url))
       (shr--blink-link))
      (t
       (browse-url url (xor new-window browse-url-new-window-flag))))))