Add anonymous access support for private repositories (backend) (#33257)

Follow #33127

This PR add backend logic and test for "anonymous access", it shares the
same logic as "everyone access", so not too much change.

By the way, split `SettingsPost` into small functions to make it easier
to make frontend-related changes in the future.

Next PR will add frontend support for "anonymous access"

models/migrations/v1_24/v318.go

@@ -0,0 +1,17 @@
+// Copyright 2025 The Gitea Authors. All rights reserved.
+// SPDX-License-Identifier: MIT
+
+package v1_24 //nolint
+
+import (
+	"code.gitea.io/gitea/models/perm"
+
+	"xorm.io/xorm"
+)
+
+func AddRepoUnitAnonymousAccessMode(x *xorm.Engine) error {
+	type RepoUnit struct { //revive:disable-line:exported
+		AnonymousAccessMode perm.AccessMode `xorm:"NOT NULL DEFAULT 0"`
+	}
+	return x.Sync(&RepoUnit{})
+}