Why doesn't the authorization flag change after logging in?

Question

Python

I implemented registration/authorization on the simplest site. The problem is that after the user has logged in, I cannot replace the "login" link with the "logout" link in the template.
To do this, I use a model attribute that is mixed into it using UserMixin. The attribute itself is called is_anonymous and is used in the template like this:

{% if current_user.is_anonymous %}
    <a href="{{ url_for('registration') }}">Регистрация</a>
    <a href="{{ url_for('login') }}">Вход</a>               
{% else %}
    <a href="{{ url_for('logout') }}">Выход</a>
{% endif %}

However, regardless of whether the user is authenticated or not, this attribute is always set to True.
Here is my model:

from app import db, login

import datetime

from werkzeug.security import generate_password_hash, check_password_hash
from flask_login import UserMixin, LoginManager


class User(UserMixin, db.Model):
    __tablename__ = 'users'

    id =            db.Column(db.Integer, primary_key=True)
    username =      db.Column(db.String(40), unique=True, nullable=False)
    password_hash = db.Column(db.String(128), nullable=False)
    reg_date_utc =  db.Column(db.DateTime, nullable=False, default=datetime.datetime.utcnow())
    upd_date_utc =  db.Column(db.DateTime, nullable=False, default=datetime.datetime.utcnow())
    email =         db.Column(db.String(40))
    desc =          db.Column(db.Text)
    is_active =     db.Column(db.Boolean, default=False) 

@login.user_loader
def load_user(id):
    return User.query.get(int(id))

here is the route:

from flask import render_template, request, url_for, redirect, flash
from flask_login import current_user, login_user, logout_user, login_required

from app import app, db
from app.forms import RegistrationForm, LoginForm
from app.models import User

...
.....

@app.route('/login', methods=['GET', 'POST'])
def login():
    login_form = LoginForm()

    if request.method == 'POST' and login_form.validate_on_submit():
        user = User.query.filter_by(email=request.form['email']).first()
        if user is None or not user.check_password(request.form['password']):
            flash('Неверные авторизационные данные')
            return redirect(url_for('login'))
        else:
            login_user(user)
            flash('Вы вошли')
            return redirect(url_for('index'))

    return render_template('login.html', title='Вход', form=login_form)

here is the package initialization:

from flask import Flask
from config import Config
from flask_sqlalchemy import SQLAlchemy
from flask_migrate import Migrate
from flask_login import LoginManager

app = Flask(__name__)
app.config.from_object(Config)

db = SQLAlchemy(app)
migrate = Migrate(app, db)

login = LoginManager(app)
login.login_view = 'login'

from app import routes, models

Flask-login itself is installed.
Please tell me what is wrong and where to look for the error. The fact is that I did all this based on a popular tutorial and in the past similar project, the authorization system worked without problems.
Here is a link to the repository if needed.