Using Python Datetime Module to Calculate the Next Year When a User-Input Date Will Occur by Factoring in the Leap Year. the Code Has an Error

This program is supposed to take the date_string parameter in the format of "year-month-day", and use the add_year function to calculate the next year that this date will occur (it's 4 years later for the 29th of February during Leap Year, and 1 year later for all other dates).

There's an error in the code which is resulting in the wrong answer. Instead of the actual date in the result, the code generates "yyyy-mm-dd" every single time.

import datetime
from datetime import date

def add_year(date_obj):
  try:
    new_date_obj = date_obj.replace(year = date_obj.year + 1)
  except ValueError:
    # This gets executed when the above method fails, 
    # which means that we're making a Leap Year calculation
    new_date_obj = date_obj.replace(year = date_obj.year + 4)
  return new_date_obj

def next_date(date_string):
  # Convert the argument from string to date object
  date_obj = datetime.datetime.strptime(date_string, r"%Y-%m-%d")
  next_date_obj = add_year(date_obj)

  # Convert the datetime object to string, 
  # in the format of "yyyy-mm-dd"
  next_date_string = next_date_obj.strftime("yyyy-mm-dd")
  return next_date_string

today = date.today()  # Get today's date
print(next_date(str(today))) 
# Should return a year from today, unless today is Leap Day

print(next_date("2021-01-01")) # Should return 2022-01-01
print(next_date("2020-02-29")) # Should return 2024-02-29