Fix LFS route mock, realm, middleware names (#32488)

1. move "internal-lfs" route mock to "common-lfs"
2. fine tune tests
3. fix "realm" strings, according to RFC:
https://datatracker.ietf.org/doc/html/rfc2617:
    * realm       = "realm" "=" realm-value
    * realm-value = quoted-string
4. clarify some names of the middlewares, rename `ignXxx` to `optXxx` to
match `reqXxx`, and rename ambiguous `requireSignIn` to `reqGitSignIn`

services/context/context.go

@@ -65,6 +65,9 @@ type Context struct {
 type TemplateContext map[string]any
 
 func init() {
+	web.RegisterResponseStatusProvider[*Base](func(req *http.Request) web_types.ResponseStatusProvider {
+		return req.Context().Value(BaseContextKey).(*Base)
+	})
 	web.RegisterResponseStatusProvider[*Context](func(req *http.Request) web_types.ResponseStatusProvider {
 		return req.Context().Value(WebContextKey).(*Context)
 	})