Extract auth middleware from service (#27028)

Related #27027

Extract the router logic from `services/auth/middleware.go` into
`routers/web` <-> `routers/common` <-> `routers/api`.

routers/common/auth.go

@@ -0,0 +1,45 @@
+// Copyright 2022 The Gitea Authors. All rights reserved.
+// SPDX-License-Identifier: MIT
+
+package common
+
+import (
+	user_model "code.gitea.io/gitea/models/user"
+	"code.gitea.io/gitea/modules/context"
+	"code.gitea.io/gitea/modules/web/middleware"
+	auth_service "code.gitea.io/gitea/services/auth"
+)
+
+type AuthResult struct {
+	Doer        *user_model.User
+	IsBasicAuth bool
+}
+
+func AuthShared(ctx *context.Base, sessionStore auth_service.SessionStore, authMethod auth_service.Method) (ar AuthResult, err error) {
+	ar.Doer, err = authMethod.Verify(ctx.Req, ctx.Resp, ctx, sessionStore)
+	if err != nil {
+		return ar, err
+	}
+	if ar.Doer != nil {
+		if ctx.Locale.Language() != ar.Doer.Language {
+			ctx.Locale = middleware.Locale(ctx.Resp, ctx.Req)
+		}
+		ar.IsBasicAuth = ctx.Data["AuthedMethod"].(string) == auth_service.BasicMethodName
+
+		ctx.Data["IsSigned"] = true
+		ctx.Data[middleware.ContextDataKeySignedUser] = ar.Doer
+		ctx.Data["SignedUserID"] = ar.Doer.ID
+		ctx.Data["IsAdmin"] = ar.Doer.IsAdmin
+	} else {
+		ctx.Data["SignedUserID"] = int64(0)
+	}
+	return ar, nil
+}
+
+// VerifyOptions contains required or check options
+type VerifyOptions struct {
+	SignInRequired  bool
+	SignOutRequired bool
+	AdminRequired   bool
+	DisableCSRF     bool
+}